Related papers: Neural-HSS: Hierarchical Semi-Separable Neural PDE…

In this paper we propose an efficient deep learning encoder-decoder network for performing Harmonic-Percussive Source Separation (HPSS). It is shown that we are able to greatly reduce the number of model trainable parameters by using a…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…

Mesh-based simulations provide high-fidelity solutions to partial differential equations (PDEs), but achieving such accuracy typically requires fine meshes, leading to substantial computational overhead. Super-resolution techniques aim to…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Deep neural networks (DNNs) exploit many layers and a large number of parameters to achieve excellent performance. The training process of DNN models generally handles large-scale input data with many sparse features, which incurs high…

Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…

Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are…

Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…

This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional…

Humans are able to recognize structured relations in observation, allowing us to decompose complex scenes into simpler parts and abstract the visual world in multiple levels. However, such hierarchical reasoning ability of human perception…

The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…

The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years,…

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…

The design of efficient hardware accelerators for high-throughput data-processing applications, e.g., deep neural networks, is a challenging task in computer architecture design. In this regard, High-Level Synthesis (HLS) emerges as a…

The numerical solution of partial differential equations (PDEs) is fundamental to scientific and engineering computing. In the presence of strong anisotropy, material heterogeneity, and complex geometries, however, classical iterative…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that incorporate physical constraints. In this work, we introduce…

Data-driven deep learning methods like neural operators have advanced in solving nonlinear temporal partial differential equations (PDEs). However, these methods require large quantities of solution pairs\u2014the solution functions and…

Approximate solutions of partial differential equations (PDEs) obtained by neural networks are highly affected by hyper parameter settings. For instance, the model training strongly depends on loss function design, including the choice of…