The research paper titled "DP-GEN: A concurrent learning platform for the generation of

reliable deep learning based potential energy models" introduces DP-GEN, an open-source
platform designed to automate and optimize the generation of deep learning-based
interatomic potential energy surface (PES) models. Here is a detailed explanation:

🌟 1. Motivation and Context

In molecular simulations, accuracy vs. efficiency is a major challenge:

 DFT-based ab initio molecular dynamics (AIMD) is accurate but computationally

expensive (limited to small systems and short timescales).

 Empirical force fields are fast but lack accuracy and generalizability.

Machine Learning (ML)-based PES models like Deep Potential (DP) aim to offer DFT-level
accuracy with force-field-like efficiency. However, the data generation process (i.e.,
selecting representative atomic configurations for training) is still manual and suboptimal.

🚀 2. What is DP-GEN?

DP-GEN (Deep Potential Generator) is a concurrent learning platform that:

 Automates the generation of ML-PES models.

 Minimizes human intervention and computational cost.

 Iteratively performs three core steps:

1. Exploration: Sample atomic configurations using MD simulations driven by a

current DP model.

2. Labeling: Select configurations with high uncertainty and compute DFT-based

energies/forces.

3. Training: Retrain the DP model using the updated dataset.

These steps form a feedback loop to improve the model progressively.

🔁 3. Methodology Overview

🔍 Exploration:

 Uses MD simulations (via LAMMPS) driven by the DP model.

 An ensemble of models is trained (differing in initialization).

  The force prediction variance among models is used as an error indicator to identify
uncertain configurations.

🧠 Labeling:

 Selected uncertain configurations are labeled using DFT software like VASP, Quantum
ESPRESSO, CP2K, or Gaussian.

 These ab initio results are added to the training dataset.

📈 Training:

 DeePMD-kit is used to train deep neural network PES models.

 DP model predicts total energy as a sum over atomic contributions.

 Embedding networks ensure rotational, translational, and permutational

invariance.

🛠️ 4. Software Architecture

DP-GEN includes:

 Scheduler: Orchestrates the 3-step concurrent learning loop.

 Task Dispatcher: Manages job submission, monitoring, and result collection on

various computational platforms (HPCs, cloud).

It supports job managers like SLURM, PBS, and LSF and can run across CPU/GPU systems
and cloud environments.

🧠 5. Case Study: Cu (Copper)

They used DP-GEN to create a general-purpose DP model for Copper, covering a wide
thermodynamic range:

 48 iterations were run.

 Out of 25 million configurations, only ~7,600 (0.03%) were selected for labeling.

 LAMMPS was used for exploration, VASP for DFT labeling, and DeePMD-kit for
training.

The resulting DP model was tested on:

 Equilibrium properties (atomization energy, volume)

 Elastic constants
  Defect formation energies

 Surface energies

 Equation of State (EOS)

 Phonon spectra

Results matched closely with DFT and experiment, often outperforming MEAM (Modified
Embedded Atom Method).

📊 6. Advantages of DP-GEN

 Efficient: Reduces labeling to only essential configurations.

 Accurate: Achieves near-DFT accuracy over a broad configuration space.

 Flexible: Supports multiple simulation codes and hardware platforms.

 Scalable: Can explore large and diverse configuration spaces.

📌 7. Limitations & Future Work

 Initial configuration setup and early exploration still need human guidance.

 Currently tailored to the DeePMD-kit and needs adaptation for other ML-PES
approaches.

 Plans include integrating with platforms like AiiDA for broader workflow automation
and data sharing.

📘 Conclusion

DP-GEN is a powerful and automated framework for developing reliable, transferable

machine-learned potentials. It addresses a critical gap in data generation for ML-PES
modeling by integrating exploration, labeling, and training into a seamless loop. Its
successful application to copper demonstrates its potential for wide adoption in materials
and molecular modeling.
The paper titled “Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy
of Quantum Mechanics” (Phys. Rev. Lett. 120, 143001) by Zhang et al. introduces the DPMD
method—a breakthrough in simulating molecular systems with quantum mechanical
accuracy and classical MD efficiency. Here is a detailed breakdown:

🔍 1. Background and Motivation

Problem:

 Ab initio molecular dynamics (AIMD) methods like DFT are accurate but
computationally expensive (limited to small systems and short timescales).

 Empirical force fields (FFs) are faster but suffer from limited accuracy and poor
transferability.

Goal:

 Combine accuracy of DFT with the scalability of force fields using machine learning
(ML).

💡 2. What is DPMD?

Deep Potential Molecular Dynamics (DPMD) is a machine learning-based method that

constructs potential energy surfaces (PES) and interatomic forces using a deep neural
network (DNN) trained on DFT data.

Key Features:

 Based on many-body potential.

 Learns from DFT-calculated energies and forces.

 Preserves physical symmetries: translational, rotational, and permutational.

 Scales linearly with system size.

🧠 3. Architecture and Methodology

3.1 Energy Decomposition:

 Total energy: E=∑iEiE = \sum_i E_iE=∑iEi

 EiE_iEi: Energy contribution from local environment of atom iii

3.2 Local Frame and Input Representation:

  For each atom:

o A local coordinate frame is constructed.

o Neighboring atoms within a cutoff radius RcR_cRc are considered.

o Inputs include inverse distances 1/Rij1/R_{ij}1/Rij and projected coordinates

xij/Rij2,yij/Rij2,zij/Rij2x_{ij}/R_{ij}^2, y_{ij}/R_{ij}^2, z_{ij}/R_{ij}^2xij/Rij2,yij
/Rij2,zij/Rij2

o Neighbors are sorted by species and distance.

3.3 Deep Neural Network (DNN):

 Feedforward architecture with 5 hidden layers.

 Layer sizes: 240 → 120 → 60 → 30 → 10 nodes.

 Activation function: tanh

 Output: atomic energy EiE_iEi

🧠 4. Training Details

Loss Function:

A weighted sum of energy, force, and virial errors:

L=pϵΔϵ2+pf3N∑i∣ΔFi∣2+pξ9∣∣Δξ∣∣2L = p_\epsilon \Delta\epsilon^2 + \frac{p_f}{3N} \sum_i

|\Delta F_i|^2 + \frac{p_\xi}{9} ||\Delta \xi||^2L=pϵΔϵ2+3Npfi∑∣ΔFi∣2+9pξ∣∣Δξ∣∣2

 Δ\DeltaΔ: deviation from DFT data

 pϵ,pf,pξp_\epsilon, p_f, p_\xipϵ,pf,pξ: tunable weights

 Training strategy: Start with force-dominant, then shift emphasis to energy and virial
for better convergence.

Optimization:

 Uses the Adam optimizer for efficient training.

🔬 5. Evaluation and Test Systems

5.1 Systems Studied:

 Extended Systems:

o Liquid water (path-integral MD)

 o Ice Ih (classical and path-integral MD)

 Finite Systems:

o Small organic molecules (e.g., benzene, aspirin, ethanol)

5.2 Accuracy Metrics:

 Forces: RMSE ~ 25–45 meV/Å

 Energies: ~0.7–1 meV per molecule

 Matches or outperforms GDML benchmarks.

5.3 Physical Property Predictions:

 Radial Distribution Functions (RDFs)

 Angular Distribution Functions (ADFs)

 Bond orientation order parameters (Q₆)

 DPMD-generated trajectories closely match AIMD results.

⚙️ 6. Performance and Scalability

 DPMD shows linear scaling with system size.

 Much faster than DFT (orders of magnitude).

 Outperforms empirical models like TIP3P for water in accuracy, and rivals them in
speed post-training.

⚠️ 7. Limitations and Considerations

 Discontinuities in forces can occur due to sharp cutoff and neighbor sorting—
mitigated by thermostats.

 Long-range electrostatics not explicitly modeled (although implicitly included if

present in training data).

 Can be extended with explicit Coulomb terms if necessary.

🔚 8. Conclusion and Impact

 DPMD bridges the gap between DFT-level accuracy and force-field-level speed.

 Enables accurate simulations of large systems over long timescales.

  Opens possibilities for:

o Training on high-level quantum chemistry or QMC data.

o Coarse-grained models using ML.

 Represents a paradigm shift in molecular simulation.

The paper titled "Active Learning of Uniformly Accurate Interatomic Potentials for
Materials Simulation" by Linfeng Zhang et al. (Phys. Rev. Materials 3, 023804, 2019)
presents a systematic method called DP-GEN (Deep Potential Generator) to automatically
generate machine learning interatomic potentials with ab initio accuracy and high
efficiency. Here's a detailed explanation of its content and significance:

🔍 1. Problem and Motivation

 In materials modeling, accurate interatomic potentials are essential for reliable

molecular dynamics (MD) simulations.

 Ab initio methods (like DFT) are accurate but computationally expensive.

 Empirical force fields (e.g., EAM, MEAM) are fast but lack accuracy and
generalizability.

 Machine learning potentials can bridge this gap but still require a well-chosen
training dataset—this is expensive and difficult.

✅ Challenge: How to train an ML-based potential energy surface (PES) with minimal DFT
calculations and ensure uniform accuracy across the configuration space?

💡 2. Solution: DP-GEN Framework

DP-GEN is an active learning workflow comprising three core components:

1. Exploration using MD simulations with a tentative potential.

2. Labeling (DFT calculations) for only informative structures.

3. Training a deep neural network-based potential (Deep Potential model).

This loop continues until the PES becomes uniformly accurate.

🧠 3. Application Systems

The method is applied to:

 Pure Al (aluminum)

 Pure Mg (magnesium)

 Al-Mg alloys

The models generated are tested on a wide range of material properties, such as:

 Energies and volumes

 Defect formation energies

 Elastic constants

 Melting point

 Phonon dispersion

 Surface energies

⚙️ 4. Technical Details

A. Deep Potential (DP) Model:

 Total energy is decomposed: E=∑iEiE = \sum_i E_iE=∑iEi, where EiE_iEi is a deep

neural network (DNN) function of the local atomic environment.

 Embedding ensures physical symmetries (translational, rotational, and permutational

invariance).

 Trained using DeePMD-kit on energy and force data from DFT.

B. Sampler:

 DPMD (MD with DP model) explores diverse configurations.

 Uses structures at varying temperatures (50 K to 2000 K) and random perturbations

to span configuration space.

C. Indicator:

 To determine if a configuration is "known" or "unknown," multiple models are

trained with different initial weights.

 Model deviation (standard deviation of predicted forces across the ensemble) is

used as an uncertainty indicator.
  High deviation → send for DFT labeling.

📊 5. Key Results

A. Accuracy vs DFT and MEAM

Property DP vs DFT DP vs MEAM

Atomization energy ≈ DFT Better

Elastic constants ≈ DFT Better

Melting point ≈ DFT Better

Surface energies ≈ DFT Better

Phonon dispersion ≈ DFT Better

Liquid RDF and diffusion ≈ DFT MEAM fails

✅ DP reproduces DFT with high fidelity and much better than MEAM, especially in non-
equilibrium or liquid states.

B. Training Efficiency

 Out of 650 million configurations explored, only ~0.0044% (~28,000) required

expensive DFT labeling—thanks to active learning.

🔬 6. Transferability to Alloys

 Tested on 28 Mg-Al alloy structures from the Materials Project (not part of training
data).

 DP performs well on:

o Formation energies

o Elastic constants

o Vacancy/interstitial energies

o Surface energies

 Suggests strong transferability and generalization of the trained model.

📌 7. Advantages of DP-GEN
  Data efficiency: Minimizes expensive DFT calculations.

 Automation: Reduces human intervention in dataset construction.

 Generalization: High transferability to unseen structures.

 Modularity: Sampling, training, and labeling components can be updated

independently.

⚠️ 8. Limitations and Future Work

 No mathematical guarantee that the indicator always captures model failures.

 In complex systems with rare events or high energy barriers, better sampling
strategies or enhanced techniques (e.g., metadynamics) may be needed.

 Future plans:

o Apply to materials with different bonding (e.g., ceramics, polymers).

o Integrate with enhanced sampling and genetic algorithms.

📚 9. Conclusion

DP-GEN demonstrates how active learning and deep neural networks can be used to
automate the generation of highly accurate interatomic potentials for both pure elements
and complex alloys. It achieves DFT-level accuracy with only a tiny fraction of DFT effort,
paving the way for routine, large-scale, and accurate molecular simulations across materials
science.

The research paper “Uncertainty-driven dynamics for active learning of interatomic

potentials” (Nature Computational Science, 2023) introduces a novel Uncertainty-Driven
Dynamics Active Learning (UDD-AL) approach for generating machine-learned interatomic
potentials efficiently and accurately.

🧠 1. Background & Motivation

 ML-based interatomic potentials aim to replicate quantum-level accuracy (like DFT)

at much lower computational cost.
  However, data generation for training these models remains expensive and
inefficient.

 Active Learning (AL) improves efficiency by sampling only high-value configurations

based on model uncertainty.

 Traditional AL methods use standard molecular dynamics (MD) or metadynamics

but struggle with either efficiency or overfitting.

🔥 Motivation:

 Improve the sampling of important, diverse configurations (especially near

transition states or underrepresented regions).

 Avoid unnecessary high-temperature MD that distorts molecular structures.

🔁 2. What is UDD-AL?

🧠 UDD-AL = Uncertainty-Driven Dynamics + Active Learning

 Key idea: Use the model's own uncertainty to bias MD simulations toward regions
of configuration space where the model is weak.

 This biasing helps escape low-energy traps and guides MD to sample high-
uncertainty (high-information) configurations.

How It Works:

1. Train ensemble of ML models (e.g., neural networks like ANI).

2. Use ensemble variance (σ²_E) in energy predictions as an uncertainty indicator.

3. Add a bias potential based on uncertainty:

Ebias(σE2)=A[e−σE2NMNAB2−1]E_{\text{bias}}(\sigma^2_E) = A \left[ e^{-

\frac{\sigma^2_E}{N_M N_A B^2}} - 1 \right]Ebias(σE2)=A[e−NMNAB2σE2−1]

o A: bias magnitude (tunes energy barrier height).

o B: bias width (tunes force influence).

4. Run biased MD simulations using:

Total Potential=E^+Ebias\text{Total Potential} = \hat{E} +

E_{\text{bias}}Total Potential=E^+Ebias

5. When the uncertainty threshold (ρ) is crossed, stop MD and add the configuration to
the training set.
🧠 3. Case Studies

🧠 (A) Glycine Conformational Sampling

 Glycine: Simple but challenging due to multiple conformers and moderate barriers
(2.5–3.5 kcal/mol).

 Compared UDD-AL (350 K) with standard MD-AL at:

o 350 K (low-T)

o 600 K (moderate-T)

o 1000 K (high-T)

🔍 Observations:

 UDD-AL @ 350 K achieved similar or better sampling efficiency than 600–1000 K

MD.

 Unlike high-T MD, UDD-AL retains low-energy structures while exploring high-energy
paths.

 Root Mean Square Error (RMSE) of UDD-trained model was lowest across multiple
test sets.

 UMAP projection showed UDD-AL reached previously inaccessible conformations.

💧 (B) Proton Transfer in Acetylacetone

 Focused on rare proton transfer between oxygen atoms.

 Compared three methods:

o 350 K MD (no transfer observed)

o 620 K MD (48 transfers)

o 350 K UDD (90 transfers)

🔍 Results:

 UDD enabled reaction sampling at low temperature without globally disturbing

molecular geometry.

 High-T MD caused widespread structural distortion (increased bond length variance).

 UDD localized bias in chemically relevant transition regions, not global energy
increase.
📊 4. Advantages of UDD-AL

Feature UDD-AL High-T MD Standard MD-AL

Samples rare events (TSs) ✅ Yes ✅ Yes (but distorted) ❌ Rarely

Retains low-energy conformations ✅ Yes ❌ Skipped ✅ Yes

Efficiency in AL convergence ✅ High Moderate ❌ Low

Requires CVs ❌ No ❌ No ❌ No

Structural fidelity ✅ High ❌ Low ✅ High

⚙️ 5. Technical Summary

 ML Model: ANI-type neural networks (3 hidden layers; 768:32:16:8:1).

 Uncertainty metric (ρ): standard deviation normalized per atom.

 Bias tuning: A ~ barrier height; B ~ variance of interatomic forces.

 Training data: Glycine (1,280 AL conformers); Acetylacetone (pre-trained ANI-1x).

 Training: Adam optimizer, learning rate annealing, early stopping.

🧠 6. Limitations and Future Work

 Manual tuning of bias parameters (A, B) is still needed.

 Uncertainty metric (ρ) could be made more adaptive.

 Promising to integrate UDD with:

o Enhanced sampling (e.g., weighted ensemble dynamics)

o Other ML models (e.g., GAP, MTP, SchNet)

📌 7. Conclusion

The paper presents a novel and general strategy to improve active learning in molecular
simulations:
  UDD-AL enables accurate, efficient, and physically realistic data generation for ML
potentials.

 It combines exploration of chemically relevant space and model uncertainty

without compromising structural integrity.

 This method is especially powerful for transition states, low-temperature systems,

and temperature-sensitive reactions.

📄 Title: Active learning of neural network potentials for rare events

Published in: Digital Discovery, 2024

Authors: Gang Seob Jung, Jong Youl Choi, and Sangkeun Matthew Lee (Oak Ridge National
Laboratory)

🧠 1. Background and Motivation

Problem:

 Neural Network Potentials (NNPs) have achieved high accuracy for potential energy
surfaces (PESs).

 However, they fail catastrophically outside their training domain, especially for rare
events such as:

o Bond breaking

o Phase transitions

o Material failure

Challenge:

 Standard MD + NNPs do not capture rare events well because these events:

o Are underrepresented in training data

o Require enhanced sampling and uncertainty-aware data selection

💡 2. Solution: Enhanced Active Learning Workflow

Goal:

Develop a NNP training strategy that can:

  Accurately simulate rare mechanical bond-breaking events

 Be data-efficient (reduce DFT/DFTB calculations)

 Be transferable across molecules and strain rates

Key Techniques Used:

 Steered Molecular Dynamics (SMD): Applies external forces to drive bond breaking.

 Active Learning (AL): Iteratively adds only “informative” data to the training set.

 Uncertainty Quantification (UQ): Uses model disagreement (ensembles) to detect

unknown regions.

 Data Augmentation: Adds small noise to configurations to explore local PES.

 Similarity Screening: Avoids redundant data by comparing geometric and energy

differences.

⚙️ 3. Methodology

Simulation Setup:

 Molecule: Hexane (C₆H₁₄)

 Initial model trained on 2000 MD frames at 500 K

 Target event: Bond breaking under tension

 Reference simulation: SMD using DFTB (Density Functional Tight Binding)

Active Learning Loop:

1. Train NNP (using TorchANI or SchNet)

2. Run SMD using NNP to simulate bond breaking

3. Use UQ to select high-uncertainty frames

4. Apply similarity filtering and data augmentation

5. Label selected configurations (with DFTB)

6. Retrain NNP, repeat until convergence

🧠 4. Key Results

🔧 Activation Energy Estimation:

  Reference DFTB SMD gives ~6.3 eV activation energy.

 Initial NNP trained only on MD data underestimates this (~1.0 eV).

 Using AL:

o Final NNP achieves activation energy error < 1 kcal/mol (~0.043 eV).

o Needs only ~3350 total configurations—about half of DFTB-SMD-only

approach.

🔄 Transferability:

 Final NNP trained on hexane is moderately transferable to:

o Other alkane chains (C₂–C₁₁)

o Different strain rates

 Best transfer performance for molecules with similar internal bond environments
(e.g., C₇, C₈)

🧠 Model Comparison:

 TorchANI (AEV-based): Stable and accurate after active learning

 SchNet (message-passing): Accurate initially, but becomes unstable in later AL

iterations

o Shows unphysical predictions in bond breaking

o Fails to generalize after active learning

📊 5. Key Innovations

Component Novelty

Uncertainty quantification Ensemble-based, standard deviation of predictions

Data selector Combines UQ, similarity check, and noise-augmented sampling

Inherited training set Improves convergence and reduces fluctuations

Model training Balanced loss between energy and force predictions

🧠 6. Practical Insights
  Training error ≠ physical accuracy: Even low MAE doesn’t ensure correct rare event
dynamics.

 SMD with NNP + AL is much faster than full DFTB SMD (10× speedup).

 Ensemble size matters: More NNPs in the ensemble improves uncertainty estimates
and AL stability.

🧠 7. Limitations and Future Work

 Still requires careful manual tuning (e.g., number of new data per iteration,
augmentation strength).

 Transferability depends on how similar test configurations are to training data.

 Further improvements needed for long chains, 2D materials, and complex reactions.

🧠 8. Conclusion

This work presents a powerful, data-efficient active learning framework for developing
NNPs that can simulate rare, high-barrier events with quantum accuracy. The proposed
enhancements (UQ, ensemble models, inherited data selection, similarity filtering)
significantly reduce computational cost while maintaining or even improving accuracy.

It serves as a reference workflow for applying machine learning potentials to materials with
mechanical failure, catalysis, or complex reaction dynamics.

The research paper titled "Machine Learning Potentials for Heterogeneous Catalysis" by
Amir Omranpour, Jan Elsner, K. Nikolas Lausch, and Jörg Behler (ACS Catalysis, 2025) is a
comprehensive perspective article that explores the current state, methods, applications,
and challenges of machine learning potentials (MLPs) in the field of heterogeneous
catalysis.

Here is a detailed explanation of the key points:

🔍 1. Motivation and Context

 Heterogeneous catalysis is essential in numerous industrial and environmental

processes (e.g., ammonia synthesis, fuel cells, petrochemical refining).
  While DFT and ab initio molecular dynamics (AIMD) provide atomic-level accuracy,
their computational cost limits system size and simulation times.

 MLPs offer a solution by replicating DFT-level accuracy for larger systems and longer
timescales, making it feasible to simulate complex catalytic reactions.

⚙️ 2. Machine Learning Potentials (MLPs)

MLPs learn the potential energy surface (PES) from DFT data and can predict energies and
forces for new configurations much faster.

Types of MLPs (Physical Perspective):

 1st generation: Low-dimensional, rigid models for fixed surfaces.

 2nd generation: High-dimensional NNPs (e.g., HDNNP, GAP, DeePMD) using local
atomic environments.

 3rd generation: Add environment-dependent charges to model electrostatics.

 4th generation: Include global information to model long-range charge transfer and
nonlocal interactions.

Types of MLPs (Mathematical Perspective):

1. Descriptor-based + regression (HDNNP, GAP, DeePMD)

2. Symmetric basis + linear regression (MTP, ACE)

3. Message-passing neural networks (MPNNs) that learn representations (e.g., SchNet,

NequIP, Allegro, MACE)

🧠 3. Applications in Heterogeneous Catalysis

A. Clusters and Surfaces

 MLPs simulate metal clusters, nanoparticles, and surface reconstruction.

 Examples:

o CO₂ dissociation on Cu nanoclusters (DeePMD)

o Pt-Rh and Cu-Au alloy behavior (ACE, HDNNP)

o Surface melting and catalytic activity predictions

B. Gas-Surface Interactions

 MLPs model adsorption, scattering, and dissociation dynamics.

  Examples:

o O₂ on Al(111), N₂ on Fe(111), CH₄ on Ni(111)

o Accurate reaction barriers, sticking probabilities, and vibrational excitations

o Ammonia decomposition in the Haber-Bosch process

C. Solid-Liquid Interfaces

 Essential for electrocatalysis and solvent effects.

 MLPs capture:

o Water dissociation, proton transfer, hydration structure

o Systems like TiO₂, ZnO, Cu, Al₂O₃, and IrO₂

o Realistic interface modeling at picosecond to nanosecond scales

🔬 4. Challenges and Open Problems

A. Data Efficiency

 Active learning (e.g., query-by-committee) is essential to avoid expensive brute-force

DFT sampling.

 Equivariant neural networks (e.g., NequIP) help reduce data needs.

B. Transferability

 MLPs may fail outside training space.

 Transfer learning and pre-trained “foundation models” are potential solutions.

C. Reference DFT Accuracy

 GGA DFT is common but often insufficient.

 Training on higher-level methods (e.g., hybrid functionals, RPA, CCSD(T)) is desirable

but computationally expensive.

D. Long-Range and Nonlocal Interactions

 Local MLPs fail to capture long-range forces (e.g., charge transfer in doped oxides).

 3G/4G MLPs and explicit correction schemes (e.g., D3, TS) are needed.

E. Electrochemical Modeling

 External fields and constant potential simulations are still challenging.

  First steps: modeling electric fields and polarization effects with MLPs.

F. Excited State Dynamics and Nonadiabatic Effects

 Most MLPs are trained on ground-state PES.

 Representing multiple PESs, spin states, and nonadiabatic coupling remains an open
research frontier.

🔭 5. Outlook and Future Directions

 Integration with enhanced sampling methods (e.g., metadynamics, umbrella

sampling)

 Automation of active learning loops

 Hybrid QM/MLP/FF models to reduce cost and increase accuracy

 Large-scale simulations for catalytic materials under realistic (operando) conditions

 Advances in ML architectures (e.g., Allegro, MACE) will further expand capabilities

📌 Summary Table of MLP Use Cases

Application Area Techniques Used Example Systems

Cluster Catalysis HDNNP, DeePMD, ACE Cu, Pt, Au, Rh clusters

Gas–Surface Dynamics NN PES + MD, SGP, MPNNs O₂, H₂, CH₄ on metals

TiO₂, ZnO, Al₂O₃, Pt, IrO₂ in

Solid–Liquid Interfaces DeePMD, GAP
water

Metadynamics, umbrella
Proton Transport ZnO, CeO₂, TiO₂, MXenes
sampl.

Electrochemical
DeepWannier, external fields Pt, Au, BiVO₄, TiO₂, graphene
Interfaces

The paper titled “Perspective: Atomistic simulations of water and aqueous systems with
machine learning potentials” (J. Chem. Phys. 160, 170901, 2024) by Amir Omranpour, Pablo
Montero De Hijes, Jörg Behler, and Christoph Dellago offers a comprehensive overview of
the development, application, and future prospects of machine learning potentials (MLPs)
in simulating water and aqueous systems at the atomic scale.

🧠 1. Motivation

Water is central to Earth’s systems—geologically, climatically, and biologically. Its unique

properties stem from a complex hydrogen bonding network. Traditional simulations have
used:

 Empirical force fields: Efficient but limited in accuracy and reactivity.

 Ab initio methods (e.g., DFT): Accurate but computationally demanding.

MLPs aim to combine the accuracy of quantum methods with the efficiency of empirical
models, making it possible to simulate large, complex, and reactive aqueous systems over
long timescales.

🔬 2. Machine Learning Potentials (MLPs)

Evolution of MLPs:

1. 1st generation: Low-dimensional NNs for diatomic molecules and small systems.

2. 2nd generation: High-dimensional NNs (e.g., HDNNP, DeePMD) using local atomic
environments.

3. 3rd generation: Include long-range electrostatics via machine-learned partial charges

(e.g., PhysNet, TensorMol).

4. 4th generation: Global charge equilibration models for charge transfer and nonlocal
effects (e.g., CENT, QRNN).

Key Methods:

 HDNNPs: Sum over atomic contributions with environment-dependent energies.

 DeePMD: Uses local frames and neural networks for atomic environments.

 GAP (Gaussian Approximation Potentials): Based on kernel methods and SOAP

descriptors.

 Message Passing Neural Networks (MPNNs) and Graph Neural Networks (GNNs):
Learn descriptors during training.

🌊 3. Applications to Aqueous Systems

A. Water Clusters

 Benchmark systems to test MLP accuracy.

 Include studies of neutral and protonated clusters, many trained on CCSD(T) or MP2
data.

 Used to develop environment-dependent electrostatics and vibrational spectra.

B. Bulk Water and Ice

 Studies of:

o Density anomaly (ice less dense than liquid water).

o Phase diagrams, vibrational spectra, and dielectric constants.

o Nuclear quantum effects (NQEs) using path-integral MD.

 Tools: HDNNPs, DeePMD, EANNs, and GNNs.

 MLPs enable simulations with thousands of atoms for nanoseconds, impossible with
AIMD.

C. Liquid–Vapor Interface

 Interface structure, orientation of water dipoles.

 Spectroscopic calculations (IR, Raman, SFG).

 Effects of long-range interactions explicitly modeled with MLP extensions.

D. Electrolyte Solutions

 Ion hydration, pH effects, and nuclear quantum effects.

 Simulations of NaOH, NaCl, CsI, Zn²⁺, F⁻, SO₄²⁻ solutions.

 Captured proton transfer mechanisms, hydration shell dynamics, and ionic

conductivity.

E. Water–Solid Interfaces

 Systems: Cu, ZnO, TiO₂, Pt, IrO₂, GaP, Fe₃O₄, etc.

 Applications:

o Dissociation and recombination of water.

o Interfacial hydrogen bonding and charge transfer.

o Proton transport, surface restructuring, and catalysis.

 MLPs allow reactive modeling on solid–liquid interfaces with near-DFT accuracy.

F. Confined Water

 Water in carbon nanotubes, MoS₂, boron nitride, and between graphene sheets.

 Studied for transport, ion confinement, friction, and vibrational spectra.

G. Reactions in Solution

 SN2 reactions, urea decomposition, enzyme catalysis.

 Computation of free energy profiles and solvation dynamics.

 Coarse-grained models (CGNet) also explored.

⚙️ 4. Methodological Developments

 Training: Requires diverse, representative data (often thousands of DFT

configurations).

 Active Learning: Reduces data cost by selecting only informative configurations.

 Long-Range Interactions: Addressed via physical models and learned electrostatics.

 Transferability: Foundation models and improved descriptors (e.g., equivariant

GNNs) aim to improve this.

📈 5. Impact and Future Outlook

Advantages of MLPs:

 Ab initio accuracy with empirical-level speed

 Reactivity (unlike most force fields)

 Scalable to large systems and long times

 Suited for studying complex aqueous phenomena: phase transitions,

electrochemistry, catalysis

Challenges:

 Poor extrapolation outside training domain.

 Need for extensive and diverse training data.

 Complexity in building “boxed” MLPs (plug-and-play models).

Future Directions:

 Integration with advanced sampling (e.g., enhanced sampling, generative models).

  Better treatment of electron densities, polarization, and charge transfer.

 Use in predictive simulations for catalysis, batteries, and environmental processes.

📌 Conclusion

This paper establishes that machine learning potentials have revolutionized our ability to
simulate water and aqueous systems. They now enable:

 Atomistic accuracy on chemical reactions and properties.

 Long-time, large-system simulations across phases and interfaces.

 Exploration of systems previously out of reach using classical or quantum methods

alone.

MLPs now stand as essential tools for modern computational chemistry and materials
science.

“Active learning meets metadynamics: Automated workflow for reactive machine learning
potentials”
Authors: Omranpour et al. (2024)
Published in: [Provide journal if needed—likely J. Chem. Theory Comput. or similar]

🧠 1. Motivation

Modern machine-learned interatomic potentials (MLIPs) allow simulation of chemical

reactions at quantum mechanical (QM) accuracy with much greater computational
efficiency. However:

 Building accurate MLIPs for chemical reactions is challenging because they require
sampling transition states, reactive intermediates, and rare configurations.

 Manual intervention is often needed to find these structures or guide sampling—

slowing down development.

💡 2. Goal of the Paper

To create a fully automated, robust, and accurate workflow that combines:

  Active Learning (AL): to minimize data requirements by selecting only the most
informative configurations.

 Enhanced Sampling via Well-Tempered Metadynamics (WTMetaD): to sample rare

events like transition states.

 A novel method: WTMetaD-IB (Inherited Bias) to speed up convergence and

improve exploration.

The workflow builds MLIPs without prior knowledge of the reaction mechanism or
transition state (TS).

🔁 3. Workflow Summary

The proposed WTMetaD-IB + Active Learning (AL) workflow includes:

1. Initial Data Sampling: A short MD or metaD run to initialize.

2. ML Model Training: Train a MLIP (linear ACE in the paper) using DFT or semi-
empirical data.

3. Metadynamics with Inherited Bias: Run WTMetaD using inherited bias from
previous runs to accelerate sampling of new regions.

4. Uncertainty Estimation: Use ensemble MLIPs to detect high-uncertainty

configurations.

5. Data Selection:

o Filter configurations by energy, diversity, and uncertainty.

o Label selected frames with QM methods.

6. Loop Until Convergence.

Result: A high-fidelity MLIP suitable for free energy calculations and long-time dynamics.

🧠 4. Case Studies (Recap)

The workflow is validated on three increasingly complex systems:

🔷 R1. SN2 Reaction (F⁻ + CH₃Cl in implicit solvent)

 Goal: Compare WTMetaD-IB to “downhill” AL (which uses a known TS).

 Findings: WTMetaD-IB samples more broadly and recovers the transition region
without prior TS knowledge. Yields better PES and TS energetics.
🔷 R2. Methyl Shift Rearrangement (Gas phase)

 System: 2,2-dimethylisoindene to 1,2-dimethylindene

 Goal: Validate against AIMD-based umbrella sampling results.

 Findings: MLIP reproduces the free energy barrier (~28 kcal/mol) with high accuracy.
Data-efficient: 395 QM points vs thousands in AIMD.

🔷 R3. Glycosylation Reaction in explicit solvent

 Realistic, complex case: 280-atom system in DCM solvent.

 Captures SN1/SNi mechanistic competition and temperature-dependent ion-pairing.

 Accurate reproduction of free energy surface, stereoselectivity, and mechanism

matching experimental results.

📈 5. Key Results

Metric Result (SN2) Methyl Shift Glycosylation

Energy MAE (meV/atom) ~2.1 ~1.5 ~0.6

Force MAE (meV/Å) ~40–50 <50 ~36.5

Accuracy of Barrier Excellent <1 kcal/mol Matches experiment

MLIP Size <350 samples <400 ~570 + DFT labeling

Speedup vs DFT/DFTB ~100×–25000× ~100× ~25000×

🔬 6. Technical Components

 ML Model Used: Linear ACE (Atomic Cluster Expansion)

 Uncertainty Estimation: Ensemble learning (5 models), using force std. dev.

 Enhanced Sampling: WTMetaD with adaptive bias potential

 Data Filtering:

o Discard redundant or uninformative frames.

o Enforce diversity (based on SOAP kernel) and uncertainty thresholds.

🔭 7. Key Innovations

Innovation Impact

Inherited bias accelerates convergence, ensures smoother

WTMetaD-IB
exploration.

No need to guess TS structures; MLIP discovers them via

TS-free AL
metaD + UQ.

Auto-labeling via
Reduces QM calculations to only informative points.
Uncertainty

Generalized Framework Works from gas phase to explicit solvent reactions.

⚠️ 8. Limitations and Outlook

 Currently limited to a single collective variable (CV); extending to multi-dimensional

CVs would improve exploration.

 CV choice still manual; could be automated via reaction discovery tools.

 Further work needed to:

o Scale to multi-step catalysis

o Include electronic excitation effects

o Generalize across chemical families (e.g., drug-like molecules)

📌 9. Conclusion

This paper presents a powerful and fully automated workflow for training MLIPs for chemical
reactions, using a combination of:

 Uncertainty-driven data selection (active learning)

 Enhanced sampling (metadynamics)

 Inherited bias for reusability and efficiency

It successfully enables reactive simulations at QM accuracy with massive speedups and

without manual TS labeling, applicable across reaction types and environments.
The research article titled “PAL – Parallel Active Learning for Machine-Learned Potentials”
presents a novel, modular, and scalable framework called PAL, designed to automate and
parallelize the process of active learning (AL) for training machine learning potentials
(MLPs). The work was developed by researchers at the Karlsruhe Institute of Technology and
aims to overcome the inefficiencies and manual interventions commonly present in
traditional AL workflows for scientific simulations.

🧠 1. Motivation

In atomistic simulations and related scientific fields, machine-learned interatomic potentials

(MLPs) trained on quantum mechanical data (like DFT) are gaining popularity. However:

 Creating a representative dataset is difficult.

 Standard active learning methods are sequential and human-dependent.

 They don’t use modern computational resources efficiently (like GPUs and multi-
node clusters).

Thus, the need arises for a parallel, scalable AL workflow that minimizes human
intervention while maximizing throughput and adaptability across domains.

💡 2. The PAL Framework

PAL (Parallel Active Learning) is an open-source, Python-based library that uses MPI
(Message Passing Interface) to manage multiple active learning tasks simultaneously.

🔁 Architecture

PAL is based on five core modular components (kernels):

1. Prediction Kernel

o Uses ML models to infer energies/forces or target properties.

o Can use multiple models (e.g. SchNet, MACE, NequIP).

o Provides uncertainty estimation via query-by-committee.

2. Generator Kernel

o Generates new configurations using MD, transition state search, or

optimization.

o Receives predicted values and uncertainty from the prediction kernel.

 o Can decide whether to continue trajectories based on uncertainty (“patience”
strategy).

3. Oracle Kernel

o Computes ground truth labels using quantum mechanical methods (e.g. DFT,
TD-DFT, CFD).

o Multiple oracles can run in parallel to label high-uncertainty configurations.

4. Training Kernel

o Trains ML models on labeled data.

o Updates weights periodically and shares them with prediction kernel.

o Early stopping and retraining logic included.

5. Controller Kernel

o Coordinates communication, scheduling, and data flow.

o Centralizes decisions on uncertainty, labeling, and convergence.

The key innovation is that all these modules run in parallel, asynchronously—unlike
traditional AL which is sequential (generate → label → train → predict).

🔬 3. Case Studies & Applications

PAL was demonstrated in four distinct domains, showing its versatility:

🔷 1. Photodynamics of Organic Semiconductors

 Molecule: 3-Methyl-4′-phenyl-diphenylsulfone

 ML model: Fully connected neural networks (NNs)

 Oracle: TDDFT at B3LYP/6-31G*

 Task: Simulate excited state dynamics

 Outcome: Efficient generation of training data using uncertainty-driven labeling;

model improves via parallel retraining

🔷 2. Hydrogen Atom Transfer (HAT) in Biological Systems

 System: Collagen-based radical migration

 ML model: GNNs (SchNet, Allegro, MACE)

 Oracle: Turbomole at DFT/BMK/def2-TZVPD

  Task: Model bond breaking and radical migration under stress

 Outcome: Achieved chemical accuracy for reaction barriers using dynamic and
continuous labeling/training

🔷 3. Bismuth Inorganic Clusters

 System: Small bismuth clusters with variable charges

 ML model: GNNs (SchNet, MACE)

 Oracle: Turbomole at DFT/TPSS/dhf-TZVP

 Task: Model reactivity and redox behavior

 Outcome: Extended MLPs to rare, heavy-element clusters with charge state variation

🔷 4. Thermo-fluid Flow Optimization

 Domain: Heat transfer and drag in fluid channels

 ML model: CNNs as surrogates for CFD simulations

 Oracle: OpenFOAM CFD solver

 Generator: Particle Swarm Optimization (PSO)

 Outcome: Efficient optimization and surrogate model development, drastically

reducing CFD simulation needs

⚙️ 4. Technical Capabilities

 Modular: Each kernel is independent and user-configurable.

 Asynchronous Parallelization: All tasks—generation, prediction, labeling, and

training—run in parallel.

 MPI-based Communication: Efficient data flow even on HPC clusters.

 Dynamic Labeling: Labeling decisions based on model uncertainty and active

feedback.

 Flexible Oracles: Supports both high-accuracy (DFT) and low-cost (xTB, CFD) ground
truth generators.

📊 5. Performance Gains & Speedup

PAL drastically improves performance:

  Photodynamics: Speedup through parallel TDDFT and batch MD.

 CFD optimization: Achieves 3× speedup by balancing computation across modules.

 Oracle Bottlenecks: Workaround via flexible retraining and rolling datasets.

Estimated speedup examples:

 When oracle and training times are comparable, PAL can double throughput.

 For balanced modules, speedup approaches 3×.

 For large-scale labeling (e.g., DFT), speedup improves linearly with more processors.

🔭 6. Future Directions

 Integration with more scheduling systems beyond SLURM.

 Real-time monitoring (e.g., GPU usage, memory).

 More plug-and-play kernel blueprints for broader scientific use.

 Community contributions encouraged (GitHub: PAL Repository)

📌 7. Conclusion

PAL is a powerful, general-purpose parallel active learning platform tailored for the scalable
and automated development of machine-learned potentials and surrogate models across:

 Chemistry

 Materials science

 Fluid dynamics

 Biology

By leveraging parallelism and uncertainty-based decision-making, PAL minimizes redundant

computations, maximizes model learning rate, and broadens the applicability of ML in
simulation-heavy scientific disciplines.