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This research applies Physics-Informed Neural Networks (PINNs) to recover parameters in the Caldeira-Leggett quantum Brownian oscillator model using partial moment traces. By enforcing physical constraints like fluctuation-dissipation relations and positive semi-definite covariance structures, the method achieves stable parameter recovery that outperforms traditional Kalman-EM approaches on synthetic data. The work demonstrates a practical convergence of machine learning techniques with quantum open-system dynamics for system identification.
Partial-Moment PINNs for Caldeira--Leggett Parameter Learning in Quantum Brownian Motion
arXiv:2608.23093v1 Announce Type: new Abstract: We study parameter recovery in the Caldeira--Leggett (quantum Brownian) oscillator from partial moment traces. Our model is a moment-level PINN that predicts the five first/second moments and enforces the linear CL/HPZ ODEs by automatic differentiation. Physical structure is imposed through a PSD (Cholesky) covariance head, high-temperature CL assumptions with $D_{xp}\approx0$, and fluctuation--dissipation ties between $D_{pp}$ and $\gamma$. On synthetic CL data with channels ${\mu_x,\sigma_{xx},\sigma_{xp}}$, the constrained variant recovers $(\omega,\gamma)$ accurately, stabilizes $D_{pp}$, and achieves low rollout error compared to finite differences and Kalman--EM (expectation--maximization) with exact Van Loan discretization. Fisher-style checks confirm that diffusion needs at least one variance observable, and sparse $\sigma_{pp}$ ``anchors'' restore conditioning. We also show that the same PINN can learn time-varying HPZ coefficients.
Abstract:We study parameter recovery in the Caldeira--Leggett (quantum Brownian) oscillator from partial moment traces. Our model is a moment-level PINN that predicts the five first/second moments and enforces the linear CL/HPZ ODEs by automatic differentiation. Physical structure is imposed through a PSD (Cholesky) covariance head, high-temperature CL assumptions with $D_{xp}\approx0$, and fluctuation--dissipation ties between $D_{pp}$ and $\gamma$. On synthetic CL data with channels ${\mu_x,\sigma_{xx},\sigma_{xp}}$, the constrained variant recovers $(\omega,\gamma)$ accurately, stabilizes $D_{pp}$, and achieves low rollout error compared to finite differences and Kalman--EM (expectation--maximization) with exact Van Loan discretization. Fisher-style checks confirm that diffusion needs at least one variance observable, and sparse $\sigma_{pp}$ ``anchors'' restore conditioning. We also show that the same PINN can learn time-varying HPZ coefficients.
4 pages, 2 figures. Published in the 2026 International Joint Conference on Neural Networks (IJCNN), IEEE World Congress on Computational Intelligence (WCCI 2026)
Quantum Physics (quant-ph); Machine Learning (cs.LG)
arXiv:2608.23093 [quant-ph]
(or arXiv:2608.23093v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.23093 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 162 words
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