Related papers: Meta-PDE: Learning to Solve PDEs Quickly Without a…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…
In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to…
The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…
We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…
We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…
There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…
Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle…
We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep…
We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed method is built upon four essential components: (i) a…
In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…
We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing PDEs by combining neural operators with either simple iterative solvers, e.g., Jacobi and Gauss-Seidel, or with Krylov methods, e.g., GMRES and…
Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for…
Standard meta-learning for representation learning aims to find a common representation to be shared across multiple tasks. The effectiveness of these methods is often limited when the nuances of the tasks' distribution cannot be captured…
When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…
Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
This article reviews meta-learning also known as learning-to-learn which seeks rapid and accurate model adaptation to unseen tasks with applications in highly automated AI, few-shot learning, natural language processing and robotics. Unlike…