Related papers: Neural Integral Equations

We propose Self-Supervised Implicit Attention (SSIA), a new approach that adaptively guides deep neural network models to gain attention by exploiting the properties of the models themselves. SSIA is a novel attention mechanism that does…

Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…

Recent advances in deep neural networks have been developed via architecture search for stronger representational power. In this work, we focus on the effect of attention in general deep neural networks. We propose a simple and effective…

Given two large lists of records, the task in entity resolution (ER) is to find the pairs from the Cartesian product of the lists that correspond to the same real world entity. Typically, passive learning methods on such tasks require large…

The Monge-Amp\`ere equation is a fundamental fully nonlinear elliptic partial differential equation that finds extensive applications across multiple disciplines. This study proposes a novel physics-informed neural network integrated with…

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…

Deep neural networks can be powerful tools, but require careful application-specific design to ensure that the most informative relationships in the data are learnable. In this paper, we apply deep neural networks to the nonlinear…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…

Imitation learning (IL) has proven to be an effective method for learning good policies from expert demonstrations. Adversarial imitation learning (AIL), a subset of IL methods, is particularly promising, but its theoretical foundation in…

Estimating individual treatment effect (ITE) from observational graph data is crucial for decision-making in the fields such as commerce and medicine. This task is challenging due to interference, where individual outcomes can be influenced…

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the…

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

Solving stiff ordinary differential equations (StODEs) requires sophisticated numerical solvers, which are often computationally expensive. In general, traditional explicit time integration schemes with restricted time step sizes are not…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…

We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator learning models, the proposed approach employs an encoder to…

Dense associative memories (DAM), are widespread models in artificial intelligence used for pattern recognition tasks; computationally, they have been proven to be robust against adversarial input and theoretically, leveraging their analogy…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Contemporary machine learning paradigm excels in statistical data analysis, solving problems that classical AI couldn't. However, it faces key limitations, such as a lack of integration with planning, incomprehensible internal structure,…