Related papers: Learning Neural Constitutive Laws From Motion Obse…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…

This paper focuses on representation learning for dynamic graphs with temporal interactions. A fundamental issue is that both the graph structure and the nodes own their own dynamics, and their blending induces intractable complexity in the…

This paper addresses the problem of uniqueness in learning physical laws for systems of partial differential equations (PDEs). Contrary to most existing approaches, it considers a framework of structured model learning, where existing,…

There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…

Classically, the mechanical response of materials is described through constitutive models, often in the form of constrained ordinary differential equations. These models have a very limited number of parameters, yet, they are extremely…

We present a novel architecture named Neural Physicist (NeurPhy) to learn physical dynamics directly from image sequences using deep neural networks. For any physical system, given the global system parameters, the time evolution of states…

We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

Distilling analytical models from data has the potential to advance our understanding and prediction of nonlinear dynamics. Although discovery of governing equations based on observed system states (e.g., trajectory time series) has…

Constitutive modelling is crucial for engineering design and simulations to accurately describe material behavior. However, traditional phenomenological models often struggle to capture the complexities of real materials under varying…

Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…

In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we…

We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…

Machine learning approaches informed by physics have offered new insights into the discovery of constitutive models from data, helping overcome some limitations of traditional constitutive modelling while reducing the cost of otherwise…

We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of…

We develop a data-driven framework for discovering constitutive relations in models of fluid flow and scalar transport. Under the assumption that velocity and/or scalar fields are measured, our approach infers unknown closure terms in the…

The intrinsic dynamics of an object governs its physical behavior in the real world, playing a critical role in enabling physically plausible interactive simulation with 3D assets. Existing methods have attempted to infer the intrinsic…

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…