arXiv subjects

Dan Mendels

Publications and source records attributed to Dan Mendels.

18 recordsLinked to original sources

arXiv2026

Out-of-Distribution Inverse Design of Elastic Networks with Differentiable Graph Neural Network Molecular Dynamics

Machine-learning-based inverse design can accelerate the discovery of materials with targeted properties, but conventional structure--property models often require large training datasets and generalize poorly beyond their training distribution. Here, we present a differentiable inverse design framework based on a graph neural network molecular dynamics simulator. By combining a short dynamical initialization with physics-based refinement during simulation, the framework enables optimization well beyond the conditions represented in the training data. Using disordered elastic networks, we show that a simulator trained only on non-auxetic systems with Poisson's ratios between 0.1 and 0.4 can design strongly auxetic networks with values as low as -0.3. The framework also produces stress--strain responses outside the range observed during training, creates localized mechanical defects absent from the training data, and generalizes across system size, enabling optimization of networks tested up to 5000 nodes despite being trained only on networks with fewer than 200 nodes.

physics.chem-ph↗

arXiv2026

Gradient-Based Inverse Design of Free-Energy Landscapes with Diffusion Models

Free-energy surfaces govern the populations of metastable states and the barriers that control transitions between them, making their direct optimization a central challenge in molecular and materials design. In this work, we introduce Gradient-Based Free Energy Surface Optimization (GB-FESO), an inverse design framework that uses a trained conditional diffusion model as a differentiable surrogate for the ensemble distribution. After training, the diffusion model is frozen, and the conditioning variables defining the system are optimized so that the generated ensemble reproduces a prescribed target free-energy surface. The optimization is carried out by backpropagating a distribution-level loss, based on kernel density estimates of the Kullback-Leibler divergence, through a deterministic diffusion sampling trajectory. We first validate GB-FESO on one-dimensional Gaussian ensembles, demonstrating that both continuous and relaxed discrete conditioning variables can be optimized to recover target distributions, including those outside the training domain. We then apply the method to a four-particle Lennard-Jones toy peptide exhibiting multiple metastable conformational states. In this more physically motivated setting, GB-FESO successfully optimizes the interaction parameters to reproduce target free-energy landscapes in the majority of test cases, with optimization performed either in the full internal-coordinate space or in a reduced collective-variable representation. These results establish GB-FESO as a promising first step toward an ensemble-level inverse design framework for molecular systems with prescribed thermodynamic and kinetic behavior.

physics.comp-ph↗

arXiv2026

Enabling Structure-Only Initialization and Out-of-Distribution Generalization in GNN-based Molecular Dynamics Simulators

Machine learning-based simulators offer the potential to model the dynamics of complex systems more efficiently than classical approaches, while retaining differentiability, a key property for materials design. Graph neural network (GNN)-based simulators have shown strong performance across a range of physical domains, including molecular dynamics. However, their reliance on temporal context for accurate prediction limits their use in inverse design settings, where simulations must be initialized from a single static configuration. Moreover, inverse design requires robust out-of-distribution (OOD) generalization, as candidate structures typically lie outside the training domain. Here, we address both challenges by introducing two complementary strategies that enable stable and accurate structure-only initialization of GNN-based simulations. To directly target OOD generalization, we propose an inference-time physics-based optimization framework that constrains model predictions to remain physically consistent during rollout. In addition, we introduce a differentiable, GNN-based barostat that enables accurate tracking of system dimensions and pressure, critical for capturing macroscopic responses and supporting OOD generalization. We evaluate these approaches in the context of uniaxial compression of disordered elastic networks spanning a broad range of geometries, Poisson ratios, and microscopic behaviors. We find that, together, these methods substantially improve rollout stability and enable reliable OOD generalization, including regimes with distinct, more complex dynamics than those in the training data. These results show that, when properly initialized and constrained, GNN-based simulators can serve as efficient and generalizable tools for materials discovery and structural optimization, advancing their use in materials, molecular, and dynamical system design.

physics.chem-ph↗

arXiv2026

Collective Variable-Guided Engineering of the Free-Energy Surface of a Small Peptide

Engineering the free-energy surfaces (FES) of proteins and peptides is central to controlling conformational ensembles and their responses to perturbations. However, predicting how chemical modifications such as point mutations reshape the FES and shift conformational equilibria remains challenging, particularly in data-scarce settings. Building on the Collective Variables for Free Energy Surface Tailoring (CV-FEST) framework, we develop a computational approach that leverages short, unbiased molecular dynamics trajectories to guide mutation analysis. Using the ten-residue beta-hairpin CLN025 and a systematic library of its single-point mutants, we apply Harmonic Linear Discriminant Analysis (HLDA) to extract collective variables from the conformational data. We find that the HLDA eigenvector learned solely from short wild-type trajectories provides residue-level insight into the propensity of mutations at specific positions to thermodynamically stabilize or destabilize the folded state. Extending this analysis, we show that shifts in the leading HLDA eigenvalue across mutants, a measure of changes in separability between the conformational ensembles along the HLDA coordinate, correlate strongly with mutation-induced changes in the free-energy difference between states, as reflected in melting temperatures. Benchmarked against Replica Exchange Molecular Dynamics simulations, these findings suggest a promising and computationally affordable route toward guiding the engineering of biomolecular free-energy landscapes.

physics.bio-ph↗

arXiv2026

Guiding Peptide Kinetics via Collective-Variable Tuning of Free-Energy Barriers

While recent advances in AI have transformed protein structure prediction, protein function is also strongly influenced by the thermodynamic and kinetic features encoded in its underlying free-energy surface. Here, we propose a data-efficient framework for engineering protein conformational kinetics by rationally reshaping free-energy landscapes to control transition rates. Built on the Collective Variables for Free Energy Surface Tailoring (CV-FEST) framework, the approach is validated on point mutations of the miniprotein Chignolin. The framework relies on Harmonic Linear Discriminant Analysis (HLDA)-based collective variables (CVs) constructed from short molecular dynamics trajectories confined to metastable folded and unfolded basins, requiring only limited local sampling rather than exhaustive rare-event simulations. Notably, the HLDA CV derived solely from the wild-type system provides residue-level scores that predict whether mutations at specific positions are likely to accelerate or slow unfolding transitions. Furthermore, the leading HLDA eigenvalue associated with the derived CV, a quantitative measure of the one-dimensional statistical separation between folded and unfolded ensembles, is significantly correlated with transition rates across mutations. Together, these results suggest that mutation-dependent kinetic effects can be inferred from minimal in-basin sampling, providing a practical route for guiding peptide and protein engineering through collective-variable design, free-energy surface engineering, and data-efficient molecular simulation.

physics.bio-ph↗

arXiv2026

A Non Linear Spectral Graph Neural Network Simulator for More Stable and Accurate Rollouts

Molecular dynamics (MD) simulations are a central tool in science and engineering enabling the study of dynamical behavior and the link between microscopic structure and macroscopic function. Their high computational cost, however, has motivated extensive efforts to develop accelerated alternatives. A promising approach is the use of machine-learning-based simulators that allow for substantially larger time steps than conventional MD. Among these, graph neural network (GNN)-based methods have been found to be especially attractive given that they naturally encode the inductive bias of interacting particle systems, however current architectures remain limited in accuracy and stability. In particular, standard message-passing schemes struggle to efficiently propagate long-range information. Here, we investigate whether spectral-GNN simulators can overcome these limitations by explicitly representing a simulated system in a global eigenmode basis, and therefore better capture long-range and collective behavior. Focusing on disordered elastic networks, model systems for complex materials and biological structures such as proteins, we compare spatial, linear spectral, and nonlinear spectral GNN architectures. We find that while spectral representations alone are not sufficient, nonlinear spectral models substantially outperform alternatives. By learning both the time-dependent dynamics and the mixing of eigenmodes, these models more accurately capture the system's slow, global modes, which dominate macroscopic behavior. This leads to a marked reduction in systematic particle-position error and significantly improved prediction of global physical properties.

physics.chem-ph↗

arXiv2025

Dynamical Data for More Efficient and Generalizable Learning: A Case Study in Disordered Elastic Networks

Machine learning models often require large datasets and struggle to generalize beyond their training distribution. These limitations pose significant challenges in scientific and engineering contexts, where generating exhaustive datasets is often impractical and the goal is frequently to discover novel solutions outside the training domain. In this work, we explore the use of dynamical data through a graph neural network-based simulator to enable efficient system-to-property learning and out-of-distribution prediction in the context of uniaxial compression of two-dimensional disordered elastic networks. We find that the simulator can learn the underlying physical dynamics from a small number of training examples and accurately reproduce the temporal evolution of unseen networks. Notably, the simulator is able to accurately predict emergent properties such as the Poisson's ratio and its dependence on strain, even though it was not explicitly trained for this task. In addition, it generalizes well across variations in system temperature, strain amplitude, and most significantly, Poisson's ratios beyond the training range. These findings suggest that using dynamical data to train machine learning models can support more data efficient and generalizable approaches for materials and molecular design, especially in data-scarce settings.

physics.chem-ph↗

arXiv2022

Systematic Modification of Functionality in Disordered Elastic Networks Through Free Energy Surface Tailoring

Advances in manufacturing and characterization of complex molecular systems have created a need for new methods for design at molecular length scales. Emerging approaches are increasingly relying on the use of Artificial Intelligence (AI), and the training of AI models on large data libraries. This paradigm shift has led to successful applications, but shortcomings related to interpretability and generalizability continue to pose challenges. Here, we explore an alternative paradigm in which AI is combined with physics-based considerations for molecular and materials engineering. Specifically, collective variables, akin to those used in enhanced sampled simulations, are constructed using a machine learning (ML) model trained on data gathered from a single system. Through the ML-constructed collective variables, it becomes possible to identify critical molecular interactions in the system of interest, the modulation of which enables a systematic tailoring of the system's free energy landscape. To explore the efficacy of the proposed approach, we use it to engineer allosteric regulation, and uniaxial strain fluctuations in a complex disordered elastic network. Its successful application in these two cases provides insights regarding how functionality is governed in systems characterized by extensive connectivity, and points to its potential for design of complex molecular systems.

cond-mat.soft↗

arXiv2022

Solubility of organic salts in solvent-antisolvent mixtures: A combined experimental and molecular dynamics simulations approach

We combine molecular dynamics simulations with experiments to estimate solubilities of organic salts in complex growth environments. We predict the solubility by simulations of the growth and dissolution of ions at the crystal surface kink sites at different solution concentrations. Thereby, the solubility is identified as the solution's salt concentration, where the energy of the ion pair dissolved in solution equals the energy of the ion pair crystallized at the kink sites. The simulation methodology is demonstrated for the case of anhydrous sodium acetate crystallized from various solvent-antisolvent mixtures. To validate the predicted solubilities, we have measured the solubilities of sodium acetate in-house, using an experimental setup and measurement protocol that guarantees moisture-free conditions, which is key for a hygroscopic compound like sodium acetate. We observe excellent agreement between the experimental and the computationally evaluated solubilities for sodium acetate in different solvent-antisolvent mixtures. Given the agreement and the rich data the simulations produce, we can use them to complement experimental tasks which in turn will reduce time and capital in the design of complicated industrial crystallization processes of organic salts.

cond-mat.soft↗

arXiv2021

Collective Variables for Free Energy Surface Tailoring -- Understanding and Modifying Functionality in Systems Dominated by Rare Events

We introduce a method for elucidating and modifying the functionality of systems dominated by rare events that relies on the automated tuning of their underlying free energy surface. The proposed approach seeks to construct collective variables (CVs) that encode the essential information regarding the rare events of the system of interest. The appropriate CVs are identified using Harmonic Linear Discriminant Analysis (HLDA), a machine-learning based method that is trained solely on data collected from short ordinary simulations in the relevant metastable states of the system. Utilizing the interpretable form of the resulting CVs, the critical interaction potentials that determine the system's rare transitions are identified and purposely modified to tailor the free energy surface in manner that alters functionality as desired. The applicability of the method is illustrated in the context of three different systems, thereby demonstrating that thermodynamic and kinetic properties can be tractably modified with little to no prior knowledge or intuition.

physics.comp-ph↗

arXiv2021

Solubility prediction of organic molecules with molecular dynamics simulations

We present a molecular dynamics simulation method for the computation of the solubility of organic crystals in solution. The solubility is calculated based on the equilibrium free energy difference between the solvated solute and its crystallized state at the crystal surface kink site. In order to efficiently sample the growth and dissolution process, we have carried out well-tempered Metadynamics simulations with a collective variable that captures the slow degrees of freedom, namely the solute diffusion to and adsorption at the kink site together with the desolvation of the kink site. Simulations were performed at different solution concentrations using constant chemical potential molecular dynamics and the solubility was identified at the concentration at which the free energy values between the grown and dissolved kink states were equal. The effectiveness of this method is demonstrated by its success in reproducing the experimental trends of solubility of urea and naphthalene in a variety of solvents.

cond-mat.stat-mech↗

arXiv2019

Blind search for complex chemical pathways using Harmonic Linear Discriminant Analysis

Disentangling the mechanistic details of a chemical reaction pathway is a hard problem that often requires a considerable amount of chemical intuition and a component of luck. Experiments struggle in observing short-life metastable intermediates, while computer simulations often rely upon a good initial guess. In this work, we propose a method that, from the simulations of a reactant and a product state, searches for reaction mechanisms connecting the two by exploring the configuration space through metadynamics, a well known enhanced molecular dynamics method. The key quantity underlying this search is based on the use of an approach called Harmonic Linear Discriminant Analysis which allows a systematic construction of collective variables. Given the reactant and product states, we choose a set of descriptors capable of discriminating between the two states. In order not to prejudge the results, generic descriptors are introduced. The fluctuations of the descriptors in the two states are used to construct collective variables. We use metadynamics in an exploratory mode to discover the intermediates and the transition states that lead from reactant to product. The search is at first conducted at a low theory level. The calculation is then refined and the energy of the intermediates and transition states discovered during metadynamics is computed again using a higher level of theory. The method's aim is to offer a simple reaction mechanism search procedure that helps in saving time and is able to find unexpected mechanisms that defy well established chemical paradigms. We apply it to two reactions, showing that a high level of complexity can be hidden even in seemingly trivial and small systems. The method can be applied to larger systems, such as reactions in solution or catalysis.

physics.chem-ph↗

arXiv2019

Augmented Harmonic Linear Discriminant Analysis

Many processes of scientific and technological interest are characterized by time scales that render their simulation impossible if one uses present day simulation capabilities. To overcome this challenge a variety of enhanced simulation methods has been developed. A much-used class of methods relies on the use of collective variables. The efficiency of these methods relies critically on an educated guess of the collective variables. For this reason much effort has been devoted to the construction and improvement of collective variables. Among the many methods proposed, harmonic linear discriminant analysis has proven effective. This method builds the collective coordinates solely from the knowledge of the fluctuations in the different metastable state. In this Letter we propose to improve upon the harmonic linear discriminant analysis by adding to the construction of the collective coordinates an extra bit of information, namely that of the transition state ensemble. Configurations belonging to the transition state ensemble are harnessed by the use of the spring shooting transition path sampling algorithm. We show on a challenging example that these coordinates thus augmented not only perform better in the calculation of the static properties, but also accelerate considerably the calculation of reaction rates.

cond-mat.stat-mech↗

arXiv2018

Finding Efficient Collective Variables: The Case of Crystallization

Several enhanced sampling methods such as umbrella sampling or metadynamics rely on the identification of an appropriate set of collective variables. Recently two methods have been proposed to alleviate the task of determining efficient collective variables. One is based on linear discriminant analysis, the other on a variational approach to conformational dynamics, and uses time-lagged independent component analysis. In this paper, we compare the performance of these two approaches in the study of the homogeneous crystallization of two simple metals. We focus on Na and Al and search for the most efficient collective variables that can be expressed as a linear combination of X-ray diffraction peak intensities. We find that the performances of the two methods are very similar. However, the method based on linear discriminant analysis, in its harmonic version, is to be preferred because it is simpler and much less computationally demanding.

physics.comp-ph↗

arXiv2018

Metadynamics with Discriminants: a Tool for Understanding Chemistry

We introduce an extension of a recently published method\cite{Mendels2018} to obtain low-dimensional collective variables for studying multiple states free energy processes in chemical reactions. The only information needed is a collection of simple statistics of the equilibrium properties of the reactants and product states. No information on the reaction mechanism has to be given. The method allows studying a large variety of chemical reactivity problems including multiple reaction pathways, isomerization, stereo- and regiospecificity. We applied the method to two fundamental organic chemical reactions. First we study the \ce{S_N2} nucleophilic substitution reaction of a \ce{Cl} in \ce{CH_2 Cl_2} leading to an understanding of the kinetic origin of the chirality inversion in such processes. Subsequently, we tackle the problem of regioselectivity in the hydrobromination of propene revealing that the nature of empirical observations such as the Markovinikov's rules lies in the chemical kinetics rather than the thermodynamic stability of the products.

physics.comp-ph↗

arXiv2018

Folding a Small Protein Using Harmonic Linear Discriminant Analysis

Many processes of scientific importance are characterized by time scales that extend far beyond the reach of standard simulation techniques. To circumvent this impediment a plethora of enhanced sampling methods has been developed. One important class of such methods relies on the application of a bias that is function of a set of collective variables specially designed for the problem under consideration. The design of good collective variables can be challenging and thereby constitutes the main bottle neck in the application of these methods. To address this problem, recently we have introduced Harmonic Linear Discriminant Analysis, a method to systematically construct collective variables. The method uses as input information on the metastable states visited during the process that is being considered, information that can be gathered in short unbiased MD simulations, to construct the collective variables as linear combinations of a set of descriptors. Here, to scale up our examination of the method's efficiency, we applied it to the folding of Chignolin in water. Interestingly, already before any biased simulations were run, the constructed one dimensional collective variable revealed much of the physics that underlies the folding process. In addition, using it in Metadynamics we were able to run simulations in which the system goes from the folded state to the unfolded one and back, where to get fully converged results we combined Metadynamics with Parallel Tempering. Finally, we examined how the collective variable performs when different sets of descriptors are used in its construction.

physics.comp-ph↗

arXiv2018

Path collective variables without paths

We introduce a method to obtain one-dimensional collective variables for studying rarely occurring transitions between two metastable states separated by a high free energy barrier. No previous information, not even approximated, on the path followed during the transition is needed. The only requirement is to know the fluctuations of the system while in the two metastable states. With this information in hand we build the collective variable using a modified version of Fisher's linear discriminant analysis. The usefulness of this approach is tested on the metadynamics simulation of two representative systems. The first is the freezing of silver iodide into the superionic $α$-phase, the second is the study of a classical Diels Alder reaction. The collective variable works very well in these two diverse cases.

physics.comp-ph↗

arXiv2012

Mobility and energy-transport in degenerate hopping systems

Revisiting charge transport in degenerate hopping systems we present a modification to the drift diffusion equation where instead of employing the generalized Einstein relation we add an energy flux term thus solving several inconsistencies. This leads also to the conclusion that, contrary to common belief, a constant quasi-Fermi level does not necessarily ensure zero electrical current. While we revisit the drift diffusion process in the context of degenerate hopping systems, a considerable part of the argumentation put forward can be applied generally to degenerate systems.

cond-mat.mes-hall↗