相关论文: A unified physics-informed generative operator fra…

End-to-end deep neural networks (DNNs) have become the state-of-the-art (SOTA) for solving inverse problems. Despite their outstanding performance, during deployment, such networks are sensitive to minor variations in the testing pipeline…

Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…

Reconstructing complex 3D interfaces from indirect measurements remains a grand challenge in scientific computing, particularly for ill-posed inverse problems like Electrical Impedance Tomography (EIT). Traditional shape optimization…

We propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed operator-learning Networks (Morephy-Net) to solve parametric partial differential equations (PDEs) in noisy data regimes, for both forward…

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,…

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…

Autoregressive neural PDE surrogates predict future states by repeatedly applying a learned one-step operator. This is a simple and widely used method, but small one-step errors can accumulate during long rollouts. The resulting drift often…

In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…

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),…

Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural…

Accurate real-time prediction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation methods for reconstructing initial conditions from sparse or…

Recent advances in generative artificial intelligence have had a significant impact on diverse domains spanning computer vision, natural language processing, and drug discovery. This work extends the reach of generative models into physical…

Multiphase flow simulation is critical in science and engineering but incurs high computational costs due to complex field discontinuities and the need for high-resolution numerical meshes. While Neural Operators (NOs) offer an efficient…

Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…

We propose a novel machine learning framework for solving optimization problems governed by large-scale partial differential equations (PDEs) with high-dimensional random parameters. Such optimization under uncertainty (OUU) problems may be…

Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…

Neural operators are a new type of models that can map between function spaces, allowing trained models to emulate the solution operators of partial differential equations (PDEs). This paper proposes a multigrid Fourier neural operator…

Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional,…