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Modeling the dynamics of real-world physical systems is critical for spatiotemporal prediction tasks, but challenging when data is limited. The scarcity of real-world data and the difficulty in reproducing the data distribution hinder…

This work introduces a port-Hamiltonian (PH) model for constrained mechanical systems, which is directly derived from the Lagrangian equations of motion. The present PH framework incorporates a singularity-free director representation of…

We consider the time evolution of a particle subjected to both a uniform electrostatic field F and a one-dimensional delta-function potential well. We derive the propagator K_F(x,t|x',0) of this system, directly leading to the wavefunction…

For a finite graph, we establish natural isomorphisms between eigenspaces of a Laplace operator acting on functions on the edges and eigenspaces of a transfer operator acting on functions on one-sided infinite non-backtracking paths.…

In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can…

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

The ab-initio computational treatment of electrochemical systems requires an appropriate treatment of the solid/liquid interfaces. A fully quantum mechanical treatment of the interface is computationally demanding due to the large number of…

This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…

We demonstrate how machine-learning based interatomic potentials can be used to model guest atoms in host structures. Specifically, we generate Gaussian approximation potential (GAP) models for the interaction of lithium atoms with…

In the present research, a variational technique to modifying the Poisson equation is presented, expanding its modelling capabilities to include a wider range of physical processes and resonant structures. The study examines the…

The Poisson--Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to…

Most current machine learning interatomic potentials (MLIPs) rely on short-range approximations, without explicit treatment of long-range electrostatics. To address this, we recently developed the Latent Ewald Summation (LES) method, which…

The applied potential governs lithium-intercalation and electrode passivation reactions in lithium ion batteries, but are challenging to calibrate in condensed phase DFT calculations. In this work, the "anode potential" of charge-neutral…

A new approach to the kinetic simulation of plasmas in complex geometries, based on the Particle-in- Cell (PIC) simulation method, is explored. In the two dimensional (2d) electrostatic version of our method, called the Arbitrary…

To further develop accurate and large-scale simulations of electrochemical interfaces, we propose a unified explicit electric potential framework to simultaneously predict atomic forces and electron density distributions. The framework…

Progress in the atomic-scale modelling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic…

One of the main challenges in the field of embodied artificial intelligence is the open-ended autonomous learning of complex behaviours. Our approach is to use task-independent, information-driven intrinsic motivation(s) to support…

Alignment of electrostatic potential between different atomic configurations is necessary for first-principles calculations of band offsets across interfaces and formation energies of charged defects. However, strong oscillations of this…

A typical classical interference pattern of two waves with intensities I_1, I_2 and relative phase phi = phi_2-phi_1 may be characterized by the 3 observables p = sqrt{I_1 I_2}, p cos\phi and -p sin\phi. They are, e.g. the starting point…

Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…