New exact Taylor's expansions and simple solutions to PDEs
We provide new exact Taylor's series with fixed coefficients and without the remainder. We demonstrate the usefulness of this contribution by using it to obtain very simple solutions to (non-linear) PDEs. We also apply the method to the portfolio model.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Spectral operator learning for parametric PDEs without data reliance
In this paper, we introduce the Spectral Coefficient Learning via Operator Network (SCLON), a novel operator learning-based approach for solving parametric partial differential equations (PDEs) without the need for data …
Operator learningTaylor Expansion Policy Optimization
In this work, we investigate the application of Taylor expansions in reinforcement learning. In particular, we propose Taylor expansion policy optimization, a policy optimization formalism that generalizes prior work (e.…
Off-policy evaluationreinforcement-learningReinforcement LearningReinforcement Learning (RL)AMITE: A Novel Polynomial Expansion for Analyzing Neural Network Nonlinearities
Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches s…
On power chi expansions of $f$-divergences
We consider both finite and infinite power chi expansions of $f$-divergences derived from Taylor's expansions of smooth generators, and elaborate on cases where these expansions yield closed-form formula, bounded approxi…
FormNeural Taylor Approximations: Convergence and Exploration in Rectifier Networks
Modern convolutional networks, incorporating rectifiers and max-pooling, are neither smooth nor convex; standard guarantees therefore do not apply. Nevertheless, methods from convex optimization such as gradient descent …