# Automatic Differentiation from Scratch: How PyTorch Computes Gradients in Physics-Informed Neural Networks

Published: 2026-07-16 · Updated: 2026-07-16 · Category: Research

Source page: https://www.sipply.dev/story/automatic-differentiation-from-scratch-how-pytorch-computes-1e4da65a · 中文: https://www.sipply.dev/zh/story/automatic-differentiation-from-scratch-how-pytorch-computes-1e4da65a

## Summary

A recent paper published on arXiv delves into the intricacies of PyTorch's automatic differentiation engine, particularly in the context of Physics-Informed Neural Networks (PINNs). The authors provide a thorough examination of how gradients are computed, emphasizing the necessity of dual differentiation during the training of these models. Through a detailed analysis of the computational graph, the paper elucidates the processes involved in both the forward and backward passes, using a multilayer perceptron as a case study to illustrate these concepts.

## Key takeaways

- The paper offers a deep dive into the mechanics of automatic differentiation in PyTorch.
- It highlights the importance of dual differentiation for training Physics-Informed Neural Networks.
- The use of a multilayer perceptron example aids in understanding the forward and backward pass processes.

## Why it matters

This research enhances the understanding of automatic differentiation, which is crucial for optimizing neural networks, especially in complex applications like physics-informed modeling.

- **Product managers:** For product managers, this research underscores the importance of robust gradient computation in developing reliable AI products that leverage physics-informed models.
- **Developers:** Developers can gain insights into the inner workings of PyTorch's differentiation engine, which can inform better practices in implementing and optimizing neural networks.
- **Students and job seekers:** Students and job-seekers can benefit from this research by understanding advanced concepts in machine learning, particularly in the application of neural networks to real-world physics problems.

## Sources

- [Automatic Differentiation from Scratch: How PyTorch Computes Gradients in Physics-Informed Neural Networks](https://arxiv.org/abs/2607.13042) (arXiv cs.LG, 2026-07-16)

## 中文

### 从零开始的自动微分：PyTorch如何在物理信息神经网络中计算梯度

一篇最近在arXiv上发表的论文深入探讨了PyTorch的自动微分引擎的复杂性，特别是在物理信息神经网络（PINNs）的背景下。作者详细检查了梯度计算的过程，强调了在训练这些模型时双重微分的必要性。通过对计算图的详细分析，论文阐明了前向和后向传播中涉及的过程，并使用多层感知机作为案例研究来说明这些概念。

**要点：**

- 论文深入探讨了PyTorch中自动微分的机制。
- 强调了双重微分在训练物理信息神经网络中的重要性。
- 使用多层感知机示例有助于理解前向和后向传播过程。

**为什么重要：** 这项研究增强了对自动微分的理解，这对优化神经网络至关重要，尤其是在物理信息建模等复杂应用中。

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