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We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network…
We demonstrate how deep convolutional neural networks can be trained to predict 2+1 D hydrodynamic simulation results for flow coefficients, mean-transverse-momentum and charged particle multiplicity from the initial energy density profile.…
We present an approach to numerical homogenization of the elastic response of microstructures. Our work uses deep neural network representations trained on data obtained from direct numerical simulation (DNS) of martensitic phase…
Under extreme operating conditions, characterized by high particle multiplicity and heavily overlapping shower energy deposits, classical particle flow algorithms encounter pronounced limitations in resolution, efficiency, and accuracy. To…
In this article we review the thermodynamics of liquids in the framework of the inherent structure formalism. We then present calculations of the distribution of the basins in the potential energy of a binary Lennard-Jones mixture as a…
Machine learning is used to approximate the kinetic energy of one dimensional diatomics as a functional of the electron density. The functional can accurately dissociate a diatomic, and can be systematically improved with training. Highly…
We study the quantum hard-rods model and obtain compact analytical expressions for density form factors, and a semi-analytical treatment for dynamic and static structure factors calculations, greatly reducing computational complexity. We…
A system of soft ellipsoid molecules confined between two planar walls is studied using classical Density Functional Theory (DFT). Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different…
Neural density estimators are flexible families of parametric models which have seen widespread use in unsupervised machine learning in recent years. Maximum-likelihood training typically dictates that these models be constrained to specify…
The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical and biological processes at such interfaces. Classical molecular dynamics…
Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic…
A free-energy functional that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous…
Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically…
Equations of State (EoS) for fluids have been a staple of engineering design and practice for over a century. Available EoS are based on the fitting of a closed-form analytical expression to suitable experimental data. The underlying…
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…
Aqueous lithium chloride solutions up to very high concentrations were investigated in classical molecular dynamics simulations. Various force fields based on the 12-6 Lennard-Jones model, parametrized for non-polarizable water solvent…
We represent the free energy functional by a diagrammatic series with tensorial coefficients indexed by powers of length scale. For hard cores, we obtain Percus' exact functional in one dimension and the Kierlik-Rosinberg form of…
Trainable activation functions, whose parameters are optimized alongside network weights, offer increased expressivity compared to fixed activation functions. Specifically, trainable activation functions defined as ratios of polynomials…
We present a differentiable formalism for learning free energies that is capable of capturing arbitrarily complex model dependencies on coarse-grained coordinates and finite-temperature response to variation of general system parameters.…
This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the…