Related papers: Learning Reaction-Diffusion Kinetics from Mechanic…

Kinetics of model catalytic processes proceeding on inhomogeneous surfaces is studied. We employ an extended mean-field model that takes into account surface inhomogeneities. The influence of surface diffusion of adsorbent on the kinetics…

Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models…

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…

Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Materials property predictions have improved from advances in machine learning algorithms, delivering materials discoveries and novel insights through data-driven models of structure-property relationships. Nearly all available models rely…

In this contribution, we present a new Materials Knowledge System framework for microstructure-sensitive predictions of effective stress--strain responses in composite materials. The model is developed for composites with a wide range of…

Cataloging the complex behaviors of dynamical systems can be challenging, even when they are well-described by a simple mechanistic model. If such a system is of limited analytical tractability, brute force simulation is often the only…

In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material…

Chemical reactions are the fundamental building blocks of drug design and organic chemistry research. In recent years, there has been a growing need for a large-scale deep-learning framework that can efficiently capture the basic rules of…

We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…

Predicting and enhancing inherent properties based on molecular structures is paramount to design tasks in medicine, materials science, and environmental management. Most of the current machine learning and deep learning approaches have…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

The accelerated inverse design of complex material properties - such as identifying a material with a given stress-strain response over a nonlinear deformation path - holds great potential for addressing challenges from soft robotics to…

This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special…

Coarse-grained modeling in molecular simulations serves not only to extend accessible time and length scales beyond atomistic limits, but also to reduce high-dimensional chemical data to low-dimensional representations that expose the…

We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…

Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…