Learn Singularly Perturbed Solutions via Homotopy Dynamics.

Chuqi Chen, Yahong Yang, Yang Xiang, Wenrui Hao

Abstract read

In one paragraph

Article in Proceedings of machine learning research, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

0numbers the graph read from it

0cells of the map it votes in

1citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

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3 · Its place in the literature

Who cites it

1 citing paper in PubMed.

ZENN: A thermodynamics-inspired computational framework for heterogeneous data-driven modeling.Proceedings of the National Academy of Sciences of the United States of America · 2026
Article

4 · The record

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PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

4 authors.

Chuqi ChenDepartment of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China.

Yahong YangDepartment of Mathematics, The Pennsylvania State University, PA, USA.

Yang XiangDepartment of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China.

Wenrui HaoDepartment of Mathematics, The Pennsylvania State University, PA, USA.

Funding

A pathophysiology driven spatial dynamic modeling framework for personalized prediction and precision medicineR35GM146894 · NIGMS · PENNSYLVANIA STATE UNIVERSITY, THE · PI WENRUI HAO · 2022 to 2026

$2.0M

NIGMS NIH HHS R35 GM146894

6 · The paper itself

Abstract

Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed problems is particularly challenging due to certain parameters in the PDEs that introduce near-singularities in the loss function. In this study, we overcome this challenge by introducing a novel method based on homotopy dynamics to effectively manipulate these parameters. From a theoretical perspective, we analyze the effects of these parameters on training difficulty in these singularly perturbed problems and establish the convergence of the proposed homotopy dynamics method. Experimentally, we demonstrate that our approach significantly accelerates convergence and improves the accuracy of these singularly perturbed problems. These findings present an efficient optimization strategy leveraging homotopy dynamics, offering a robust framework to extend the applicability of neural networks for solving singularly perturbed differential equations.

Identifiers

PMID41321373

PMCPMC12662737

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.