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In this paper we focus on the development of new methods suitable for efficient and reliable coarse-graining of {\it non-equilibrium} molecular systems. In this context, we propose error estimation and controlled-fidelity model reduction…
The properties of soft electronic materials depend on the coupling of electronic and conformational degrees of freedom over a wide range of spatiotemporal scales. Description of such properties requires multiscale approaches capable of, at…
The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However,…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
The necessity for accurate and computationally efficient representations of water in atomistic simulations that can span biologically relevant timescales has born the necessity of coarse-grained (CG) modeling. Despite numerous advances, CG…
We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…
Coarse-grained (CG) models are simplified representations of soft matter systems that are commonly employed to overcome size and time limitations in computational studies. Many approaches have been developed to construct and parametrise…
We propose the first, to our knowledge, coarse-grained modeling strategy for peptides where the effect of changes of the pH can be efficiently described. The idea is based on modeling the effects of the pH value on the main driving…
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
To acquire the ability to numerically study the rheology of particulate two-phase flows that lack scale separation, we present a general method to average or coarse-grain the equations of motion of a mixture of a continuous fluid of…
When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…