相关论文: Generating synthetic data for neural operators

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

Synthetic data has been hailed as the silver bullet for privacy preserving data analysis. If a record is not real, then how could it violate a person's privacy? In addition, deep-learning based generative models are employed successfully to…

In this work, we describe a novel approach to building a neural PDE solver leveraging recent advances in transformer based neural network architectures. Our model can provide solutions for different values of PDE parameters without any need…

Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

This paper investigates synthetic data generation strategies in developing generative retrieval models for domain-specific corpora, thereby addressing the scalability challenges inherent in manually annotating in-domain queries. We study…

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…

In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs),…

Training models on synthetic data has emerged as an increasingly important strategy for improving the performance of generative AI. This approach is particularly helpful for large multimodal models (LMMs) due to the relative scarcity of…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…

We develop a class of data-driven generative models that approximate the solution operator for parameter-dependent partial differential equations (PDE). We propose a novel probabilistic formulation of the operator learning problem based on…

Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…

Programming by example is the problem of synthesizing a program from a small set of input / output pairs. Recent works applying machine learning methods to this task show promise, but are typically reliant on generating synthetic examples…

Deep metric learning aims to learn embeddings that contain semantic similarity information among data points. To learn better embeddings, methods to generate synthetic hard samples have been proposed. Existing methods of synthetic hard…

We present an overview and evaluation of a new, systematic approach for generation of highly realistic, annotated synthetic data for training of deep neural networks in computer vision tasks. The main contribution is a procedural world…

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…

Solving time-dependent parametric partial differential equations (PDEs) is challenging for data-driven methods, as these models must adapt to variations in parameters such as coefficients, forcing terms, and initial conditions.…

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…