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We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs,…

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…

In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as…

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given…

Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neural operator…

Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based…

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…

This paper presents an efficient mesh deformation method based on boundary integration and neural operators, formulating the problem as a linear elasticity boundary value problem (BVP). To overcome the high computational cost of traditional…

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…

To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the…

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…

We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law…

Physics-Informed Neural Networks (PINN) are algorithms from deep learning leveraging physical laws by including partial differential equations together with a respective set of boundary and initial conditions as penalty terms into their…

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…

The brain-body-environment framework studies adaptive behavior through embodied and situated agents, emphasizing interactions between brains, biomechanics, and environmental dynamics. However, many models often treat the brain as a network…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

This work introduces an efficient novel approach for epistemic uncertainty estimation for ensemble models for regression tasks using pairwise-distance estimators (PaiDEs). Utilizing the pairwise-distance between model components, these…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…