Related papers: INO: Invariant Neural Operators for Learning Compl…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…

A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a…

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…

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…

Representing a signal as a continuous function parameterized by neural network (a.k.a. Implicit Neural Representations, INRs) has attracted increasing attention in recent years. Neural Processes (NPs), which model the distributions over…

Machine learning has witnessed substantial growth, leading to the development of advanced artificial intelligence models crafted to address a wide range of real-world challenges spanning various domains, such as computer vision, natural…

Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning…

Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving inverse problems. In this paper, we propose an invertible…

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…

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…

Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B${}^{-1}$, an inverse basis-to-basis neural operator framework that…

Solving partial differential equations with neural operators significantly reduces computational costs but remains bottlenecked by high training data requirements. Active learning offers a natural framework to mitigate this by selectively…

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…

Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We…

With deep learning gaining attention from the research community for prediction and control of real physical systems, learning important representations is becoming now more than ever mandatory. It is of extreme importance that deep…

Neural operators generally demonstrate strong predictive performance on in-distribution (ID) problems. However, a critical limitation of existing methods is their significant performance degradation when encountering out-of-distribution…

Accurately forecasting the long-term evolution of turbulence represents a grand challenge in scientific computing and is crucial for applications ranging from climate modeling to aerospace engineering. Existing deep learning methods,…

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…

We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…