Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators

• URL: http://arxiv.org/abs/2605.18883v1
• Date: Sat, 16 May 2026 05:23:41 GMT
• Title: Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators
• Abstract summary: A diffusion model trained on Hamiltonian trajectories can achieve rollout MSE near $10-3$, but the standard deviation of its energy over time is between 7500 and 36000 times larger than the ground-truth energy standard deviation, indicating a failure to preserve conservation laws.<n>We investigate this across three Hamiltonian systems: projectile motion, pendulum, and spring-mass.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A diffusion model trained on Hamiltonian trajectories can achieve rollout MSE near $10^{-3}$, but the standard deviation of its energy over time is between 7500 and 36000 times larger than the ground-truth energy standard deviation, indicating a failure to preserve conservation laws. This gap motivates our central question of whether neural networks can learn or select globally conserved quantities from physical trajectories. We investigate this across three Hamiltonian systems: projectile motion, pendulum, and spring-mass. We use a structured $T(v)+V(q)$ energy model, a black-box Conservation Discovery Network (CDN), a polynomial CDN, and a conditional diffusion baseline. The structured network reaches $R^2 \geq 0.9999$ against analytical energy on clean data, while the black-box CDN reaches $R^2 \geq 0.996$ when trained with temporal consistency plus a small alignment loss to analytical energy at $t=0$ ($λ_{\mathrm{align}}=0.2$). With $λ_{\mathrm{align}}=0$, CDN Pearson $R^2$ collapses on pendulum and spring-mass ($< 10^{-3}$), showing that temporal consistency alone is not enough to reliably identify the true energy. Under $1\%$ additive Gaussian noise, the CDN outperforms the structured model on the projectile and spring-mass systems, suggesting that the CDN may be more robust to noisy inputs in this setting. However, the polynomial CDN is sensitive to training configuration: it achieves $R^2=0.78$ under a short training schedule on the pendulum system, but reaches $R^2=0.9998$ with more training time and data, regardless of whether noise is added.

Related papers

• On trace invariance and energy-dependent entanglement in muon decay [45.88028371034407]
  We revisit a proposed correction to the muon magnetic anomaly measurement.<n>We compare it with energy-binned scans reported by the Fermilab $g-2$ collaboration.
  arXiv  Detail & Related papers  (2026-08-19T12:06:54Z)
• The Information Content of Krylov Observables: A Machine Learning Approach [0.0]
  We quantify the spread complexity $mathcalC(t)$, the discrete Wigner negativity $N(t)$, and the normalized negativity $(t)=N(t)/|S(t)|$, with $S(t)$ the survival amplitude, recently proposed as a second-moment infall probe (arXiv:2607.04065).<n>Small residual networks (16-32 neurons) and boosted trees are trained on half of $sim 57,000$ labeled evolutions spanning the GUE, GOE and Poisson ensembles, the integrable $SL
  arXiv  Detail & Related papers  (2026-07-19T17:17:21Z)
• Decoherence as Defence and the Magnitude of Noise Regularisation: A Rigorous N -Qubit Theory of Stochastic Quantum Neural Networks for Adversarially Robust Network Intrusion Detection [0.0]
  We give an $N$-qubit formulation through the master equation and its vectorised Liouvillian.<n>We prove a emphdecoherence-contraction theorem: a depolarising channel of strength.<n>We show this robustness arises from a noise-reshaped training boundary rather than from attack-time contraction.
  arXiv  Detail & Related papers  (2026-06-23T07:06:56Z)
• Sequential Physics-Constrained Neural Operator Forward Modeling for the $\ extit{Norne}$ Reservoir System [3.175986877079391]
  We develop a comprehensive framework for sequential surrogate modeling of black-oil reservoir dynamics using neural operators.<n>The application focus is the Norne benchmark reservoir, defined on a heterogeneous $46times112times22$ grid.<n>A 1000-member ensemble runs in under one minute on a single B200 GPU, giving a $sim104times$ wall-clock speedup over the OPM finite-volume simulator.
  arXiv  Detail & Related papers  (2026-05-27T17:18:39Z)
• Theta-term in Russian Doll Model: phase structure, quantum metric and BPS multifractality [45.88028371034407]
  We investigate the phase structure of the deterministic and disordered versions of the Russian Doll Model (RDM)<n>We find the pattern of phase transitions in the global charge $Q(theta,gamma)$, which arises from the BA equation.<n>We conjecture that the Hamiltonian of the RDM model describes the mixing in particular 2d-4d BPS sector of the Hilbert space.
  arXiv  Detail & Related papers  (2025-10-23T17:25:01Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma.<n>This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles.<n>We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Bayesian Inference with Deep Weakly Nonlinear Networks [57.95116787699412]
  We show at a physics level of rigor that Bayesian inference with a fully connected neural network is solvable. We provide techniques to compute the model evidence and posterior to arbitrary order in $1/N$ and at arbitrary temperature.
  arXiv  Detail & Related papers  (2024-05-26T17:08:04Z)
• Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the Born-Oppenheimer rovibrational spectrum [44.99833362998488]
  This paper calculates the potential energy curve for the state $X1Sigma+$ of the Cr$$$ dimer. It is found for the first time for the whole range of internuclear distances $R$.
  arXiv  Detail & Related papers  (2024-01-06T17:00:12Z)
• Isolated pulsar population synthesis with simulation-based inference [0.0]
  We develop a framework to model neutron star birth properties and their dynamical and magnetorotational evolution. We then follow an SBI approach that focuses on neural posterior estimation and train deep neural networks to infer the parameters' posterior distributions. Our approach represents a crucial step toward robust statistical inference for complex population synthesis frameworks.
  arXiv  Detail & Related papers  (2023-12-22T17:19:53Z)
• Neural Inference of Gaussian Processes for Time Series Data of Quasars [72.79083473275742]
  We introduce a new model that enables it to describe quasar spectra completely. We also introduce a new method of inference of Gaussian process parameters, which we call $textitNeural Inference$. The combination of both the CDRW model and Neural Inference significantly outperforms the baseline DRW and MLE.
  arXiv  Detail & Related papers  (2022-11-17T13:01:26Z)
• Bounding the Width of Neural Networks via Coupled Initialization -- A Worst Case Analysis [121.9821494461427]
  We show how to significantly reduce the number of neurons required for two-layer ReLU networks. We also prove new lower bounds that improve upon prior work, and that under certain assumptions, are best possible.
  arXiv  Detail & Related papers  (2022-06-26T06:51:31Z)
• Magnetic excitations, non-classicality and quantum wake spin dynamics in the Hubbard chain [0.0]
  Quantum Fisher information (QFI) is a witness of multipartite entanglement, and magnetic Van Hove correlations $G(r,t)$, a probe of local real-space real-time spin dynamics. We show that QFI grows with $U$ and can witness bipartite entanglement above $U=2.5$. We discuss experimental candidates for observing the $G(r,t)$ dynamics found at low $U$.
  arXiv  Detail & Related papers  (2022-03-12T03:48:21Z)
• Quantum spin solver near saturation: QS$^3_{~}$ [0.0]
  We develop a program package named QS$3$ [textipakj'u:-'es-kj'u:b] based on the (thick-restart) Lanczos method for analyzing spin-1/2 XXZ-type quantum spin models. We show the benchmark results of QS$3$ for the low-energy excitation dispersion of the isotropic Heisenberg model on the $10times10times10$ cubic lattice.
  arXiv  Detail & Related papers  (2021-07-02T07:06:34Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.