# High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2210.00518 · HTML: https://mlsanity.com/paper/2210.00518/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 30 references that are in the map.
- First posted on arXiv 2 Oct 2022.

## Builds on (most cited first, 4 of 4)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations](https://mlsanity.com/paper/1703.10230/) (2017)

## Built on by (most cited first, 2 of 2)

- [A comprehensive analysis of PINNs: Variants, Applications, and Challenges](https://mlsanity.com/paper/2505.22761/) (2025)
- [Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy](https://mlsanity.com/paper/2507.20929/) (2025)

## Abstract (arXiv)

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.