Related papers: Non-intrusive Learning of Physics-Informed Spatio-…

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design…

Modeling spatiotemporal dynamical systems is a fundamental challenge in machine learning. Transformer models have been very successful in NLP and computer vision where they provide interpretable representations of data. However, a…

Spatio-temporal data are ubiquitous in the agricultural, ecological, and environmental sciences, and their study is important for understanding and predicting a wide variety of processes. One of the difficulties with modeling spatial…

Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…

Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM)…

Designing photonic integrated circuits requires accurate electromagnetic field simulations, which remain computationally expensive even for simple device geometries. We present PIC-Flow, a generative neural surrogate that predicts…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the…

The goal of this paper is to make a strong point for the usage of dynamical models when using reinforcement learning (RL) for feedback control of dynamical systems governed by partial differential equations (PDEs). To breach the gap between…

Spatiotemporal imaging has applications in e.g. cardiac diagnostics, surgical guidance, and radiotherapy monitoring, In this paper, we explain the temporal motion by identifying the underlying dynamics, only based on the sequential images.…

The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians…

We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…

Data-driven constitutive modeling is an emerging field in computational solid mechanics with the prospect of significantly relieving the computational costs of hierarchical computational methods. Traditionally, these surrogates have been…

A data-driven framework for spatial-temporal prediction is proposed for reducing the computational cost of industrial thermal striping applications. The framework aims to efficiently identify the flow features and utilize them in…

Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…

Physics-informed methods have gained a great success in analyzing data with partial differential equation (PDE) constraints, which are ubiquitous when modeling dynamical systems. Different from the common penalty-based approach, this work…

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…

We present an inductive spatio-temporal learning framework rooted in inductive logic programming. With an emphasis on visuo-spatial language, logic, and cognition, the framework supports learning with relational spatio-temporal features…