High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks
Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed. It is shown that the proposed techniques allow to generate accurate higher order derivatives simultaneously for a set of spatial points. The calculated derivatives can then be used for data-driven solution in different ways. An application for Physics Informed Neural Networks by the well-known DeepXDE software solution in Python under Tensorflow background framework has been presented for three real-life PDEs: Burgers', Allen-Cahn and Schrodinger equations.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Succinct Differentiation of Disparate Boosting Ensemble Learning Methods for Prognostication of Polycystic Ovary Syndrome Diagnosis
Prognostication of medical problems using the clinical data by leveraging the Machine Learning techniques with stellar precision is one of the most important real world challenges at the present time. Considering the med…
Ensemble LearningDifferentiation Strategies for Acoustic Inverse Problems: Admittance Estimation and Shape Optimization
We demonstrate a practical differentiable programming approach for acoustic inverse problems through two applications: admittance estimation and shape optimization for resonance damping. First, we show that JAX-FEM's aut…
Randomized Automatic Differentiation
The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectiv…
Stochastic OptimizationVariational InferenceColors Matter: AI-Driven Exploration of Human Feature Colors
This study presents a robust framework that leverages advanced imaging techniques and machine learning for feature extraction and classification of key human attributes-namely skin tone, hair color, iris color, and vein-…
ClassificationFace DetectionReconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology
Cells with the same genome can exist in different phenotypes. and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during developme…