Chercheur qualifié · Institute of Condensed Matter and Nanosciences, UCLouvain

Materials simulation, from electrons to atoms.

Developing electronic-structure methods and machine-learning techniques, including long-range interatomic potentials, and applying them to emerging materials.

Recent work · MACE-FNO, 2026

An efficient, configuration-dependent kernel for long-range physics in machine-learning potentials

A gold dimer on aluminium-doped MgO(001) Side view of an MgO slab with a gold dimer on its surface. An aluminium dopant sits several layers below, outside the dashed circle that marks the receptive field of a local model. Rings spreading from the dopant reach the dimer. local receptive field Au₂ Al dopant
Au2 on Al-doped MgO(001), schematically. The dopant lies outside the receptive field of a one-layer local model, yet it reverses how the gold dimer binds to the surface. MACE-FNO reproduces the reversal within 5 meV per cell of DFT.

Most machine-learning interatomic potentials only see atoms within a finite cutoff. Long-range extensions couple learned sources across the cell through a kernel, but that kernel is usually fixed, either prescribed as Coulomb or learned once for all configurations.

MACE-FNO, developed with Gian-Marco Rignanese, learns the kernel with a Fourier neural operator on top of a local MACE model, from energies and forces alone. Its nonlinear form adapts the coupling between distant ions to the surrounding medium, which no fixed kernel can do once the screening varies in space. In the bulk benchmarks, this comes at a cost comparable to that of a prescribed-kernel model.

27–41%
Lower force errors than fixed-kernel models when the screening is inhomogeneous.
43% → 3%
Error in long-wavelength charge fluctuations under strong screening, from a prescribed Coulomb kernel to the learned operator.
< 3%
Extra peak memory over the local model in the bulk benchmarks.

How the Fourier neural operator captures long-range physics

  1. 01

    Local sources

    MACE reads the local environment of each atom, and a small network turns it into latent sources.

  2. 02

    Mesh

    The sources are spread onto a regular mesh, as in particle-mesh methods.

  3. 03

    Fourier layers

    In Fourier space, every wave spans the whole cell. A learned kernel weights and mixes them, and stacked nonlinear layers let it adapt to the configuration.

  4. 04

    Long-range response

    Back in real space, the response at one atom reflects sources far beyond its cutoff. Its overlap with the sources gives the energy correction.

E = EMACE + ΔEFNO, with ΔEFNO = ½ ∫ ρ · φ dr over the mesh, where ρ are the source fields and φ the response fields.

Where a fixed kernel falls short

Charge fluctuations at long wavelength

SZZ(k) of a synthetic ionic fluid under strong screening (κ = 0.5 Å⁻¹), from molecular dynamics.

  • Exact reference
  • MACE-LES, prescribed Coulomb kernel
  • MACE-FNO, learned kernel
0 0.03 0.06 0.09 0 0.2 0.4 0.6 SZZ(k) k (Å⁻¹) −43% FNO LES

The eight longest-wavelength shells of a 32 Å cell. Sampling errors are smaller than the symbols.

Data table
k (Å⁻¹)Exact referenceMACE-LESMACE-FNO
0.1960.02830.01620.0283
0.2780.03240.02740.0327
0.3400.03790.03550.0382
0.3930.04410.04430.0436
0.4390.04970.05150.0491
0.4810.05580.05900.0558
0.5550.06940.07520.0703
0.5890.07930.08300.0785

Response to a rearranged remote medium

Change in the coupling between two ions 10 to 12 Å apart when only the screening medium far from both is rearranged.

  • MACE-FNO, nonlinear
  • MACE-LES
  • CACE-SOG
−0.3 0 0.3 −0.3 −0.15 0 0.15 0.3 model change (meV/Ų) reference change (meV/Ų) FNO, slope 1.13 LES and CACE-SOG, slope 0 ideal

Dots are averages over bins of the reference change, with 40 probe sets and five training seeds pooled. LES and CACE-SOG do not respond at all.

Data table
Reference changeMACE-FNOMACE-LESCACE-SOG
−0.271−0.30800
−0.223−0.24200
−0.174−0.20600
−0.122−0.15900
−0.070−0.10000
−0.020−0.02800
0.0210.03000
0.0710.09400
0.1230.16400
0.1740.19900
0.2280.27300
0.2730.30100

Selected publications

Six highly cited papers of the last ten years. The full list of more than 60 publications is on Google Scholar.

  1. 2023
    A map of single-phase high-entropy alloys

    W. Chen, A. Hilhorst, G. Bokas, S. Gorsse, P. J. Jacques, G. Hautier · Nat. Commun. 14, 2856

  2. 2021
    Origin of the low conversion efficiency in Cu2ZnSnS4 kesterite solar cells: the actual role of cation disorder

    W. Chen, D. Dahliah, G.-M. Rignanese, G. Hautier · Energy Environ. Sci. 14, 3567

  3. 2018
    Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators

    W. Chen, G. Miceli, G.-M. Rignanese, A. Pasquarello · Phys. Rev. Mater. 2, 073803

  4. 2018
    Nonempirical hybrid functionals for band gaps and polaronic distortions in solids

    G. Miceli, W. Chen, I. Reshetnyak, A. Pasquarello · Phys. Rev. B 97, 121112(R)

  5. 2018
    Alignment of redox levels at semiconductor–water interfaces

    Z. Guo, F. Ambrosio, W. Chen, P. Gono, A. Pasquarello · Chem. Mater. 30, 94

  6. 2016
    Ab initio electronic structure of liquid water

    W. Chen, F. Ambrosio, G. Miceli, A. Pasquarello · Phys. Rev. Lett. 117, 186401

Software

MACE-FNO

A configuration-dependent long-range kernel for MACE potentials, built on Fourier neural operators.

GCMC

Grand canonical Monte Carlo with replica exchange and hybrid MC/MD for ASE-compatible potentials.

MPEA Stability

Web application that predicts the thermodynamic stability of multi-principal element alloys.

ABINIT

Bootstrap exchange-correlation kernels, vertex corrections and range-separated hybrid functionals.

Quantum ESPRESSO

Range-separated hybrid functionals.

FNV

Python package for charged-defect corrections.

Python, Fortran, Bash · PyTorch · MPI, GPU, Slurm · Git, CI/CD, Linux