Related papers: Neural network based limiter with transfer learnin…
Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…
Neural control offers strong potential for handling highly nonlinear dynamics in shipboard microgrids (SMGs), yet its black-box nature can trigger abrupt control spikes and actuator saturation during initial transient shocks. This letter…
Deep neural networks (DNNs) have been widely used in many fields such as images processing, speech recognition; however, they are vulnerable to adversarial examples, and this is a security issue worthy of attention. Because the training…
We introduce techniques for exploring the functionality of a neural network and extracting simple, human-readable approximations to its performance. By performing gradient ascent on the input space of the network, we are able to produce…
In this paper, eight different troubled cell indicators (shock detectors) are reviewed for the solution of nonlinear hyperbolic conservation laws using discontinuous Galerkin (DG) method and a WENO limiter on both structured and…
Deep learning is typically performed by learning a neural network solely from data in the form of input-output pairs ignoring available domain knowledge. In this work, the Constraint Guided Gradient Descent (CGGD) framework is proposed that…
We learn recurrent neural network optimizers trained on simple synthetic functions by gradient descent. We show that these learned optimizers exhibit a remarkable degree of transfer in that they can be used to efficiently optimize a broad…
The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to time-dependent problems can, e.g., be done by backward difference formulae (BDF) or…
The popularity of deep learning techniques renewed the interest in neural architectures able to process complex structures that can be represented using graphs, inspired by Graph Neural Networks (GNNs). We focus our attention on the…
Quantum machine learning has the potential for a transformative impact across industry sectors and in particular in finance. In our work we look at the problem of hedging where deep reinforcement learning offers a powerful framework for…
Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact…
Numerous applications necessitate the computation of numerical solutions to differential equations across a wide range of initial conditions and system parameters, which feeds the demand for efficient yet accurate numerical integration…
In this paper, we study deep neural networks (DNNs) for solving high-dimensional evolution equations with oscillatory solutions. Different from deep least-squares methods that deal with time and space variables simultaneously, we propose a…
Machine learning methods have been lately used to solve partial differential equations (PDEs) and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques…
Recurrent neural networks (RNNs) are widely used to model sequential data but their non-linear dependencies between sequence elements prevent parallelizing training over sequence length. We show the training of RNNs with only linear…
The level set method is often used to capture interface behavior in two or three dimensions. In this paper, we present a combination of local discontinuous Galerkin (LDG) method and level set method for simulating Willmore flow. The LDG…
Neural networks have proven to be efficient surrogate models for tackling partial differential equations (PDEs). However, their applicability is often confined to specific PDEs under certain constraints, in contrast to classical PDE solvers…
A class of high order asymptotic preserving (AP) schemes has been developed for the BGK equation in Xiong et. al. (2015) [37], which is based on the micro-macro formulation of the equation. The nodal discontinuous Galerkin (NDG) method with…
The study of Neural Tangent Kernels (NTKs) has provided much needed insight into convergence and generalization properties of neural networks in the over-parametrized (wide) limit by approximating the network using a first-order Taylor…
This work concerns the design and analysis of a limiting technique that allows the preservation of invariant domains for high-order numerical approximations of nonlinear hyperbolic systems of conservation laws. The method can be applied to…