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Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…
Given the inherent limitations of traditional Variational Quantum Eigensolver(VQE) algorithms, the integration of deep generative models into hybrid quantum-classical frameworks, specifically the Generative Quantum Eigensolver(GQE),…
Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit…
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For…
Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…
Partial differential equations (PDEs) play a crucial role in financial mathematics, particularly in portfolio optimization, and solving them using classical numerical or neural network methods has always posed significant challenges. Here,…
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,…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central…
Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…
A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…
Many real-world problems, like modelling environment dynamics, physical processes, time series etc., involve solving Partial Differential Equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture…
Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…
Quantum computing holds great promise for solving classically intractable problems such as linear systems and partial differential equations (PDEs). While fully fault-tolerant quantum computers remain out of reach, current noisy…
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…
The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it…
Solving high-dimensional partial differential equations (PDEs) is a major challenge in scientific computing. We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning.…
Quantum embedding is a fundamental prerequisite for applying quantum machine learning techniques to classical data, and has substantial impacts on performance outcomes. In this study, we present Neural Quantum Embedding (NQE), a method that…
Solving partial differential equations (PDEs) is a fundamental problem in science and engineering. While neural PDE solvers can be more efficient than established numerical solvers, they often require large amounts of training data that is…
This work presents a deep learning-based framework for the solution of partial differential equations on complex computational domains described with computer-aided design tools. To account for the underlying distribution of the training…