Unsupervised Neural Networks for Quantum Eigenvalue Problems
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Abstract (arXiv)
Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that identically satisfy the boundary conditions. A scanning mechanism is embedded allowing the method to find an arbitrary number of solutions. The network optimization is data-free and depends solely on the predictions. The unsupervised method is used to solve the quantum infinite well and quantum oscillator eigenvalue problems.
Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Oct 2020.
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Citing papers per year: 2021: 6; 2022: 3; 2023: 1; 2024: 1; 2025: 3; 2026: 1.
15 papers.
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- 2021Learning Size and Shape of Calabi-Yau Spacescited by 28
- 2021Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problemscited by 21
- 2022Physics-Informed Neural Networks for Quantum Eigenvalue Problemscited by 18
- 2022Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flowscited by 12
- 2024Operator SVD with Neural Networks via Nested Low-Rank Approximationcited by 12
- 2021Unsupervised Reservoir Computing for Solving Ordinary Differential Equationscited by 11
- 2025Physics-informed neural network solves minimal surfaces in curved spacetimecited by 6
- 2021A Swarm Variant for the Schr"odinger Solvercited by 2
- 2022First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfacescited by 2
- 2023On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problemcited by 2
- 2021A New Artificial Neuron Proposal with Trainable Simultaneous Local and Global Activation Functioncited by 0
- 2021Adversarial Sampling for Solving Differential Equations with Neural Networkscited by 0
3 more
- 2026PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling4 Jul 2026
- 2025Physics-Informed Neural Solvers for Periodic Quantum Eigenproblems20 Dec 2025
- 2025Physics-informed neural network solves minimal surfaces in curved spacetime13 Sep 2025
- 2025A ZeNN architecture to avoid the Gaussian trap26 May 2025
- 2024Operator SVD with Neural Networks via Nested Low-Rank Approximation6 Feb 2024
- 2023On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem15 Mar 2023
- 2022First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces8 Nov 2022
- 2022Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows1 Nov 2022
- 2022Physics-Informed Neural Networks for Quantum Eigenvalue Problems24 Feb 2022
- 2021Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems7 Dec 2021
- 2021Adversarial Sampling for Solving Differential Equations with Neural Networks20 Nov 2021
- 2021Learning Size and Shape of Calabi-Yau Spaces2 Nov 2021
- 2021Learning Size and Shape of Calabi-Yau Spacescited by 28
- 2021Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problemscited by 21
- 2022Physics-Informed Neural Networks for Quantum Eigenvalue Problemscited by 18
- 2022Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flowscited by 12
- 2024Operator SVD with Neural Networks via Nested Low-Rank Approximationcited by 12
- 2021Unsupervised Reservoir Computing for Solving Ordinary Differential Equationscited by 11
- 2025Physics-informed neural network solves minimal surfaces in curved spacetimecited by 6
- 2021A Swarm Variant for the Schr"odinger Solvercited by 2
- 2022First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfacescited by 2
- 2023On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problemcited by 2
- 2021A New Artificial Neuron Proposal with Trainable Simultaneous Local and Global Activation Functioncited by 0
- 2021Adversarial Sampling for Solving Differential Equations with Neural Networkscited by 0
12 most cited of 15 All 15 (JSON)
- 2026PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling4 Jul 2026
- 2025Physics-Informed Neural Solvers for Periodic Quantum Eigenproblems20 Dec 2025
- 2025Physics-informed neural network solves minimal surfaces in curved spacetime13 Sep 2025
- 2025A ZeNN architecture to avoid the Gaussian trap26 May 2025
- 2024Operator SVD with Neural Networks via Nested Low-Rank Approximation6 Feb 2024
- 2023On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem15 Mar 2023
- 2022First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces8 Nov 2022
- 2022Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows1 Nov 2022
- 2022Physics-Informed Neural Networks for Quantum Eigenvalue Problems24 Feb 2022
- 2021Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems7 Dec 2021
- 2021Adversarial Sampling for Solving Differential Equations with Neural Networks20 Nov 2021
- 2021Learning Size and Shape of Calabi-Yau Spaces2 Nov 2021
12 newest of 15 All 15 (JSON)