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Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required…

Self-training techniques have shown remarkable value across many deep learning models and tasks. However, such techniques remain largely unexplored when considered in the context of learning fast solvers for systems of partial differential…

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…

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…

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…

Neural operators as novel neural architectures for fast approximating solution operators of partial differential equations (PDEs), have shown considerable promise for future scientific computing. However, the mainstream of training neural…

Koopman operator theory is a popular candidate for data-driven modeling because it provides a global linearization representation for nonlinear dynamical systems. However, existing Koopman operator-based methods suffer from shortcomings in…

Fourier Neural Operators (FNOs) have emerged as promising surrogates for partial differential equation solvers. In this work, we extensively tested FNOs on a variety of systems with non-linear and non-stationary properties, using a wide…

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…

We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…

Machine Learning methods belong to the group of most up-to-date approaches for solving partial differential equations. The current work investigates two classes, Neural FEM and Neural Operator Methods, for the use in elastostatics by means…

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…

This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. The proposed framework learns an operator from the…

Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability.…

Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence.…

Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon dynamical systems. While neural operator methods such as the…

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and…

This paper addresses boundary prescribed-time stabilization of a one-dimensional heat equation with spatially and temporally varying coefficients. In contrast to asymptotic or exponential stabilization, prescribed-time stabilization ensures…

This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…

This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight…