Partial-Moment PINNs for Caldeira--Leggett Parameter Learning in Quantum Brownian Motion
2026-08-24 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explore how to figure out key parameters of a quantum system called the Caldeira–Leggett oscillator by only looking at some statistical measurements (moments). They use a specialized neural network that respects the physical laws governing the system to predict those moments and recover important parameters like frequency and damping. Their method performs better than traditional techniques on simulated data and also works when the system's parameters change over time. The study highlights the importance of certain measurements to accurately determine the system's behavior.
Caldeira–Leggett modelquantum Brownian motionmoment methodsphysics-informed neural networks (PINNs)fluctuation–dissipation theoremFisher informationKalman filterexpectation–maximizationcovariance matrixtime-varying coefficients
Authors
Krishna Bhatia
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 $γ$. On synthetic CL data with channels ${μ_x,σ_{xx},σ_{xp}}$, the constrained variant recovers $(ω,γ)$ 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 $σ_{pp}$ ``anchors'' restore conditioning. We also show that the same PINN can learn time-varying HPZ coefficients.