# STNet: Spectral Transformation Network for Solving Operator Eigenvalue Problem

arXiv: https://arxiv.org/abs/2510.23986 · HTML: https://mlsanity.com/paper/2510.23986/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Spectral Inference Networks: Unifying Deep and Spectral Learning](https://mlsanity.com/paper/1806.02215/) (2018)
- [Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach](https://mlsanity.com/paper/2002.02600/) (2020)
- [NeuralEF: Deconstructing Kernels by Deep Neural Networks](https://mlsanity.com/paper/2205.00165/) (2022)
- [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://mlsanity.com/paper/2510.22192/) (2025)
- [Physics-Informed Neural Networks for Quantum Eigenvalue Problems](https://mlsanity.com/paper/2203.00451/) (2022)
- [MILP-StuDio: MILP Instance Generation via Block Structure Decomposition](https://mlsanity.com/paper/2410.22806/) (2024)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Accelerating PDE Data Generation via Differential Operator Action in Solution Space](https://mlsanity.com/paper/2402.05957/) (2024)
- [Operator SVD with Neural Networks via Nested Low-Rank Approximation](https://mlsanity.com/paper/2402.03655/) (2024)
- [Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation](https://mlsanity.com/paper/2310.14161/) (2023)
- [Accelerating Data Generation for Neural Operators via Krylov Subspace Recycling](https://mlsanity.com/paper/2401.09516/) (2024)
- [Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems](https://mlsanity.com/paper/2209.11134/) (2022)
- [Deep Symbolic Optimization for Combinatorial Optimization: Accelerating Node Selection by Discovering Potential Heuristics](https://mlsanity.com/paper/2406.09740/) (2024)
- [Machine Learning Insides OptVerse AI Solver: Design Principles and Applications](https://mlsanity.com/paper/2401.05960/) (2024)
- [Exploiting Edited Large Language Models as General Scientific Optimizers](https://mlsanity.com/paper/2503.09620/) (2025)
- [Solving the functional Eigen-Problem using Neural Networks](https://mlsanity.com/paper/2007.10205/) (2020)
- [ChASE: Chebyshev Accelerated Subspace iteration Eigensolver for sequences of Hermitian eigenvalue problems](https://mlsanity.com/paper/1805.10121/) (2018)

## Built on by (most cited first, 3 of 3)

- [Learning Neural Operators from Partial Observations via Latent Autoregressive Modeling](https://mlsanity.com/paper/2601.15547/) (2026)
- [Learning-Guided Integration Contours Construction for Fast Large-Scale Generalized Eigensolvers](https://mlsanity.com/paper/2511.01927/) (2025)
- [Low-Fidelity FDM Spectral Guidance for Neural Eigenvalue Solvers](https://mlsanity.com/paper/2610.04695/) (2026)

## Abstract (arXiv)

Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to address this challenge by iteratively updating neural networks. These methods' performance relies heavily on the spectral distribution of the given operator: larger gaps between the operator's eigenvalues will improve precision, thus tailored spectral transformations that leverage the spectral distribution can enhance their performance. Based on this observation, we propose the Spectral Transformation Network (STNet). During each iteration, STNet uses approximate eigenvalues and eigenfunctions to perform spectral transformations on the original operator, turning it into an equivalent but easier problem. Specifically, we employ deflation projection to exclude the subspace corresponding to already solved eigenfunctions, thereby reducing the search space and avoiding converging to existing eigenfunctions. Additionally, our filter transform magnifies eigenvalues in the desired region and suppresses those outside, further improving performance. Extensive experiments demonstrate that STNet consistently outperforms existing learning-based methods, achieving state-of-the-art performance in accuracy.