Related papers: PI-MFM: Physics-informed multimodal foundation mod…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

In multi-body dynamics, the motion of a complicated physical object is described as a coupled ordinary differential equation system with multiple unknown solutions. Engineers need to constantly adjust the object to meet requirements at the…

Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…

Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression…

Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs). PIML models are increasingly built via deep neural networks (NNs) whose…

Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Control in fluid environments is an important research area with numerous applications across various domains, including underwater robotics, aerospace engineering, and biomedical systems. However, in practice, control methods often face…

The random feature method (RFM) constructs approximation spaces by initializing features from generic distributions, which provides universal approximation properties to solve general partial differential equations. However, such standard…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

Physics informed neural networks (PINNs) have recently been proposed as surrogate models for solving process optimization problems. However, in an active learning setting collecting enough data for reliably training PINNs poses a challenge.…

Physics-informed deep learning approaches have been developed to solve forward and inverse stochastic differential equation (SDE) problems with high-dimensional stochastic space. However, the existing deep learning models have difficulties…

Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…

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 work introduces Physics-informed State-space neural network Models (PSMs), a novel solution to achieving real-time optimization, flexibility, and fault tolerance in autonomous systems, particularly in transport-dominated systems such…

Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off between accuracy and computational efficiency, while existing…

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…