---
title: "Data-driven discovery of intrinsic Lie point symmetries of differential equation systems"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.08421v1"
permalink: "https://feed.astralor.com/items/itm_ddd1502fd07e213aea89e81c"
published: "2026-11-05T18:19:28.000Z"
score: 58
channel: "tech"
tags: ["Data-driven","Lie","Discovering","Admissible","Lie-bracket"]
---

# Data-driven discovery of intrinsic Lie point symmetries of differential equation systems

## 速览

Discovering continuous symmetries directly from differential-equation data can reveal geometric structure for model reduction and scientific machine learning without symbolic determining equations or a closed-form repre…

## 关键点

- Discovering continuous symmetries directly from differential-equation data can reveal geometric structure for model reduction and scientific machine learning without symbolic determining equations or a closed-form repre…
- We formulate intrinsic Lie point-symmetry discovery as an operator-theoretic problem on sampled jet-space data.
- Admissible generators are identified from a sampled determining operator and separated from redundant, solution-dependent, and geometrically trivial directions.

## 全文

Discovering continuous symmetries directly from differential-equation data can reveal geometric structure for model reduction and scientific machine learning without symbolic determining equations or a closed-form representation of the governing system. We formulate intrinsic Lie point-symmetry discovery as an operator-theoretic problem on sampled jet-space data. Admissible generators are identified from a sampled determining operator and separated from redundant, solution-dependent, and geometrically trivial directions. The framework combines prolongation, sequential subspace restrictions, and a fixed nonlinear dictionary linear in trainable coefficients. A rank-stabilization preflight test diagnoses systems whose represented intrinsic symmetry algebra does not stabilize under dictionary refinement. On a controlled differential-equation benchmark with an analytically known 11-dimensional represented intrinsic symmetry algebra, the method recovers the complete represented generator set, reproduces its Lie-bracket structure to numerical precision, and approximates a known generator beyond the training domain. Here we show that explicit intrinsic continuous-symmetry generators can be recovered from data obtained from exact or approximate differential systems.

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