Morten Ledum

• Cezar, Henrique Musseli; Bodenstein, Tilmann; Sveinsson, Henrik Andersen; Ledum, Morten; Reine, Simen & Bore, Sigbjørn Løland (2025). Learning atomic forces from uncertainty-calibrated adversarial attacks. npj Computational Materials. 11. doi: 10.1038/s41524-025-01703-5. Full text in Research Archive Show summary

  Adversarial approaches, which intentionally challenge machine learning models by generating difficult examples, are increasingly being adopted to improve machine learning interatomic potentials (MLIPs). While already providing great practical value, little is known about the actual prediction errors of MLIPs on adversarial structures and whether these errors can be controlled. We propose the Calibrated Adversarial Geometry Optimization (CAGO) algorithm to discover adversarial structures with user-assigned errors. Through uncertainty calibration, the estimated uncertainty of MLIPs is unified with real errors. By performing geometry optimization for calibrated uncertainty, we reach adversarial structures with the user-assigned target MLIP prediction error. Integrating with active learning pipelines, we benchmark CAGO, demonstrating stable MLIPs that systematically converge structural, dynamical, and thermodynamical properties for liquid water and water adsorption in a metal-organic framework within only hundreds of training structures, where previously many thousands were typically required.

• Carrer, Manuel; Cezar, Henrique Musseli; Bore, Sigbjørn Løland; Ledum, Morten & Cascella, Michele (2024). Learning Force Field Parameters from Differentiable Particle-Field Molecular Dynamics. Journal of Chemical Information and Modeling. ISSN 1549-9596. 64, p. 5510–5520. doi: 10.1021/acs.jcim.4c00564. Full text in Research Archive Show summary

  We develop ∂-HylleraasMD (∂-HyMD), a fully end-to-end differentiable molecular dynamics software based on the Hamiltonian hybrid particle-field formalism, and use it to establish a protocol for automated optimization of force field parameters. ∂-HyMD is templated on the recently released HylleraaasMD software, while using the JAX autodiff framework as the main engine for the differentiable dynamics. ∂-HyMD exploits an embarrassingly parallel optimization algorithm by spawning independent simulations, whose trajectories are simultaneously processed by reverse mode automatic differentiation to calculate the gradient of the loss function, which is in turn used for iterative optimization of the force-field parameters. We show that parallel organization facilitates the convergence of the minimization procedure, avoiding the known memory and numerical stability issues of differentiable molecular dynamics approaches. We showcase the effectiveness of our implementation by producing a library of force field parameters for standard phospholipids, with either zwitterionic or anionic heads and with saturated or unsaturated tails. Compared to the all-atom reference, the force field obtained by ∂-HyMD yields better density profiles than the parameters derived from previously utilized gradient-free optimization procedures. Moreover, ∂-HyMD models can predict with good accuracy properties not included in the learning objective, such as lateral pressure profiles, and are transferable to other systems, including triglycerides.

• Sen, Samiran; Cezar, Henrique Musseli; Ledum, Morten; Li, Xinmeng & Cascella, Michele (2024). Phase Coexistence in Hamiltonian Hybrid Particle-Field Theory Using a Multi-Gaussian Approach. Journal of Physical Chemistry B. ISSN 1520-6106. 128(47), p. 11739–11747. doi: 10.1021/acs.jpcb.4c05525. Full text in Research Archive Show summary

  This study introduces an implementation of multiple Gaussian filters within the Hamiltonian hybrid particle-field (HhPF) theory, aimed at capturing phase co-existence phenomena in mesoscopic molecular simulations. By employing a linear combination of two Gaussians, we demonstrate that HhPF can generate potentials with attractive and steric components analogous to Lennard-Jones potentials, which are crucial for modeling phase co-existence. We compare the performance of this method with the Multi-Gaussian Core Model (MGCM) in simulating liquid-gas coexistence for a single-component system across various densities and temperatures. Our results show that HhPF effectively captures detailed information on phase co-existence and interfacial phenomena, including micro-configuration transitions and increased interfacial fluctuations at higher temperatures. Notably, the phase boundaries obtained from HhPF simulations align more closely with those of Lennard-Jones systems compared to the MGCM results. This work advances the hybrid particle-field methodology to address phase co-existence without requiring modifications to the equation of state or introducing additional interaction energy functional terms, offering a promising approach for mesoscale molecular simulations of complex systems.

• Sen, Samiran; Cezar, Henrique Musseli; Ledum, Morten; Li, Xinmeng & Cascella, Michele (2024). Phase coexistence in Hamiltonian hybrid particle--field theory using a Multi-Gaussian approach. ChemRxiv. ISSN 2573-2293. doi: 10.26434/chemrxiv-2024-cm4xr-v2. Full text in Research Archive
• Ledum, Morten; Sen, Samiran; Li, Xinmeng; Carrer, Manuel; Feng, Yu & Cascella, Michele [Show all 7 contributors for this article] (2023). HylleraasMD: A Domain Decomposition-Based Hybrid Particle-Field Software for Multiscale Simulations of Soft Matter. Journal of Chemical Theory and Computation. ISSN 1549-9618. doi: 10.1021/acs.jctc.3c00134. Full text in Research Archive Show summary

  We present HylleraasMD (HyMD), a comprehensive implementation of the recently proposed Hamiltonian formulation of hybrid particle-field molecular dynamics. The methodology is based on a tunable, grid-independent length-scale of coarse graining, obtained by filtering particle densities in reciprocal space. This enables systematic convergence of energies and forces by grid refinement, also eliminating nonphysical force aliasing. Separating the time integration of fast modes associated with internal molecular motion from slow modes associated with their density fields, we enable the first time-reversible, energy-conserving hybrid particle-field simulations. HyMD comprises the optional use of explicit electrostatics, which, in this formalism, corresponds to the long-range potential in particle-mesh Ewald. We demonstrate the ability of HyMD to perform simulations in the microcanonical and canonical ensembles with a series of test cases, comprising lipid bilayers and vesicles, surfactant micelles, and polypeptide chains, comparing our results to established literature. An on-the-fly increase of the characteristic coarse-grain length significantly speeds up dynamics, accelerating self-diffusion and leading to expedited aggregation. Exploiting this acceleration, we find that the time scales involved in the self-assembly of polymeric structures can lie in the tens to hundreds of picoseconds instead of the multimicrosecond regime observed with comparable coarse-grained models.

• Sen, Samiran; Ledum, Morten; Bore, Sigbjørn Løland & Cascella, Michele (2023). Soft Matter under Pressure: Pushing Particle-Field Molecular Dynamics to the Isobaric Ensemble. Journal of Chemical Information and Modeling. ISSN 1549-9596. 63, p. 2207–2217. doi: 10.1021/acs.jcim.3c00186. Full text in Research Archive Show summary

  Hamiltonian hybrid particle–field molecular dynamics is a computationally efficient method to study large soft matter systems. In this work, we extend this approach to constant-pressure (NPT) simulations. We reformulate the calculation of internal pressure from the density field by taking into account the intrinsic spread of the particles in space, which naturally leads to a direct anisotropy in the pressure tensor. The anisotropic contribution is crucial for reliably describing the physics of systems under pressure, as demonstrated by a series of tests on analytical and monatomic model systems as well as realistic water/lipid biphasic systems. Using Bayesian optimization, we parametrize the field interactions of phospholipids to reproduce the structural properties of their lamellar phases, including area per lipid, and local density profiles. The resulting model excels in providing pressure profiles in qualitative agreement with all-atom modeling, and surface tension and area compressibility in quantitative agreement with experimental values, indicating the correct description of long-wavelength undulations in large membranes. Finally, we demonstrate that the model is capable of reproducing the formation of lipid droplets inside a lipid bilayer.

• Ledum, Morten; Carrer, Manuel; Sen, Samiran; Li, Xinmeng; Cascella, Michele & Bore, Sigbjørn Løland (2023). HylleraasMD: Massively parallel hybrid particle-field molecular dynamics in Python. Journal of Open Source Software (JOSS). 8(84). doi: 10.21105/joss.04149. Full text in Research Archive Show summary

  Molecular dynamics (MD) is a computational methodology in which the dynamical behavior of systems of interacting atoms and molecules is investigated by integrating the corresponding classical equations of motion. The analysis of the molecular trajectories yields an incredibly powerful computational microscope with atomic resolution. While prominent examples of molecular dynamics involving all-atom models exist, many systems operate on time- and lengths scales too large, precluding the use of such an approach. The intrinsic complexity of biological soft-matter systems has necessitated the development of coarse-grained (CG) MD models wherein groups of atoms are treated as individual entities. To probe experimentally relevant length- (nm–μm) and time- (ps–ms) scales, further reduction of computational complexity may be warranted through the removal of explicit particle–particle interactions in favor of particle–density field interactions. Such hybrid particle–field (hPF) models recast the interactions between particle pairs into a system of free particles interacting with an external potential dependent on the density, in analogy with self-consistent field theories. HylleraasMD (named after our affiliate centre, the Hylleraas Centre for Quantum Molecular Sciences) (HyMD) is a Python package capable of highly parallel hPF-MD simulations of a wide range of surfactants and other biological systems in a CG representation. At present, it is the only open-source implementation of the hPF formalism freely available to computational researchers.

• Ledum, Morten; Sen, Samiran; Bore, Sigbjørn Løland & Cascella, Michele (2023). On the equivalence of the hybrid particle-field and Gaussian core models. Journal of Chemical Physics. ISSN 0021-9606. 158(19). doi: 10.1063/5.0145142. Full text in Research Archive Show summary

  Hybrid particle–field molecular dynamics is a molecular simulation strategy, wherein particles couple to a density field instead of through ordinary pair potentials. Traditionally considered a mean-field theory, a momentum and energy-conserving hybrid particle–field formalism has recently been introduced, which was demonstrated to approach the Gaussian Core model potential in the grid-converged limit. Here, we expand on and generalize the correspondence between the Hamiltonian hybrid particle–field method and particle–particle pair potentials. Using the spectral procedure suggested by Bore and Cascella, we establish compatibility to any local soft pair potential in the limit of infinitesimal grid spacing. Furthermore, we document how the mean-field regime often observed in hybrid particle–field simulations is due to the systems under consideration, and not an inherent property of the model. Considering the Gaussian filter form, in particular, we demonstrate the ability of the Hamiltonian hybrid particle–field model to recover all structural and dynamical properties of the Gaussian Core model, including solid phases, a first-order phase transition, and anomalous transport properties. We quantify the impact of the grid spacing on the correspondence, as well as the effect of the particle–field filtering length scale on the emergent particle–particle correlations.

• Ledum, Morten; Bore, Sigbjørn Løland & Cascella, Michele (2020). Automated determination of hybrid particle-field parameters by machine learning. Molecular Physics. ISSN 0026-8976. 118(19-20), p. 1–12. doi: 10.1080/00268976.2020.1785571. Full text in Research Archive Show summary

  The hybrid particle-field molecular dynamics method is an efficient alternative to standard particle-based coarse grained approaches. In this work, we propose an automated protocol for optimisation of the effective parameters that define the interaction energy density functional, based on Bayesian optimisation. The machine-learning protocol makes use of an arbitrary fitness function defined upon a set of observables of relevance, which are optimally matched by an iterative process. Employing phospholipid bilayers as test systems, we demonstrate that the parameters obtained through our protocol are able to reproduce reference data better than currently employed sets derived by Flory-Huggins models. The optimisation procedure is robust and yields physically sound values. Moreover, we show that the parameters are satisfactorily transferable among chemically analogous species. Our protocol is general, and does not require heuristic a posteriori rebalancing. Therefore it is particularly suited for optimisation of reliable hybrid particle-field potentials of complex chemical mixtures, and extends the applicability corresponding simulations to all those systems for which calibration of the density functionals may not be done via simple theoretical models.

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• Ledum, Morten; Cascella, Michele & Gauss, Jurgen (2022). Hamiltonian hybrid particle–field method for biological soft matter - Efficient simulation and machine learning approaches. Universitetet i Oslo. Full text in Research Archive Show summary

  Hybrid particle–field methods couple coarse-grained particles through a density field-based intermolecular potential. This allows for large-scale and computationally efficient simulations of soft-matter systems while retaining molecular resolution. The recently introduced Hamiltonian hybrid particle–field method now also allows for rigorous energy and momentum conservation in the grid-converged regime, giving hybrid particle–field results a more solid theoretical footing. This dissertation presents the use of the Hamiltonian hybrid particle–field method for biological soft-matter simulations and outlines recent progress made through the development of new algorithmic and methodological approaches. Four research papers are presented, with topics including the implementation of the first open-source and freely accessible hybrid particle–field software, an approach for determining accurate model parameters through machine learning, the introduction of pressure control schemes, and theoretical results on the intrinsic approximations made in the hybrid scheme and their impact on the model dynamics.

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