Related papers: Guiding continuous operator learning through Physi…

The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning…

Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions.…

This work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science. Here we propose a new technique to force the positive…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

The modeling and control of complex physical systems are essential in real-world problems. We propose a novel framework that is generally applicable to solving PDE-constrained optimal control problems by introducing surrogate models for PDE…

Traditional electrostatic simulation are meshed-based methods which convert partial differential equations into an algebraic system of equations and their solutions are approximated through numerical methods. These methods are time…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

In this paper, we introduce the Spectral Coefficient Learning via Operator Network (SCLON), a novel operator learning-based approach for solving parametric partial differential equations (PDEs) without the need for data harnessing. The…

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…

We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By…

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…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…