Related papers: Fast automated adjoints for spectral PDE solvers
Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…
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…
We present a general and scalable framework for the automated discovery of optimal meta-solvers for the solution of time-dependent nonlinear partial differential equations after appropriate discretization. By integrating classical numerical…
In this work we propose an efficient stochastic plug-and-play (PnP) algorithm for imaging inverse problems. The PnP stochastic gradient descent methods have been recently proposed and shown improved performance in some imaging applications…
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…
We introduce an efficient open-source python package for the inverse design of three-dimensional photonic nanostructures using the Finite-Difference Time-Domain (FDTD) method. Leveraging a flexible reverse-mode automatic differentiation…
Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is…
We propose a PDE-based accelerated gradient algorithm for optimal feedback controls of McKean-Vlasov dynamics that involve mean-field interactions both in the state and action. The method exploits a forward-backward splitting approach and…
A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential…
Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stiff problems. We study this issue in Physics-Informed Extreme…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…
We address the problem of simultaneously recovering a sequence of point source signals from observations limited to the low-frequency end of the spectrum of their summed convolution, where the point spread functions (PSFs) are unknown. By…
Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…
We study linear abstract differential-algebraic equations (ADAEs), and we introduce an index concept which is based on polynomial growth of a~pseudo-resolvent. Our approach to solvability analysis is based on degenerate semigroups. We apply…
Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results…
This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
In this work, we propose a new deep learning-based scheme for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). The idea is to reformulate the problem as a global optimization, where the local loss…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…
PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately compute the PDE solution introduce an enormous number of…