Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations

Out-of-equilibrium quantum many-body systems exhibit rapid correlation buildup that underlies many emerging phenomena. Exact wave-function methods to describe this scale exponentially with particle number; simpler mean-field approaches neglect essential two-particle correlations. The time-dependent two-particle reduced density matrix (TD2RDM) formalism offers a middle ground by propagating the two-particle reduced density matrix (2RDM) and closing the BBGKY hierarchy with a reconstruction of the three-particle cumulant. But the validity and existence of time-local reconstruction functionals ignoring memory effects remain unclear across different dynamical regimes. We show that a neural ODE model trained on exact 2RDM data (no dimensionality reduction) can reproduce its dynamics without any explicit three-particle information -- but only in parameter regions where the Pearson correlation between the two- and three-particle cumulants is large. In the anti-correlated or uncorrelated regime, the neural ODE fails, indicating that no simple time-local functional of the instantaneous two-particle cumulant can capture the evolution. The magnitude of the time-averaged three-particle-correlation buildup appears to be the primary predictor of success: For a moderate correlation buildup, both neural ODE predictions and existing TD2RDM reconstructions are accurate, whereas stronger values lead to systematic breakdowns. These findings pinpoint the need for memory-dependent kernels in the three-particle cumulant reconstruction for the latter regime. Our results place the neural ODE as a model-agnostic diagnostic tool that maps the regime of applicability of cumulant expansion methods and guides the development of non-local closure schemes. More broadly, the ability to learn high-dimensional RDM dynamics from limited data opens a pathway to fast, data-driven simulation of correlated quantum matter.

Robustly optimal dynamics for active matter reservoir computing

We study the information processing abilities of active matter in the reservoir computing (RC) paradigm, using a model that is externally driven to infer the future state of a chaotic signal. The simulated system closely follows a previously reported model. We uncover an exceptional dynamical regime of agent dynamics that has been overlooked heretofore. It appears robustly optimal across varying physical parameters and inference tasks, thus providing valuable insights into computation and inference with physical systems more generally. The ability to form effective mechanisms for information processing are primarily determined by the system's own intrinsic relaxation abilities. These are identifiable when probing the system without a specific inference goal and manifest when testing minimalistic single-particle reservoirs. The regime that achieves optimal computation is situated just below the critical damping threshold, involving a microscopic dynamical relaxation with multiple stages. The optimal system is adaptable under chaotic external driving, due to a diversity in response mechanisms that emerge like rapid alternations between quasi-stationary and highly nonlinear dynamical states. Both coherent and incoherent dynamics contribute to their operation, partly at dissimilar scales of space and delay time. Correlations on agent dynamics can indicate the best-performing regimes and onsets of tight relationships between the responding system and the fluctuating driver. As this model of computation is interpretable in physical terms, it facilitates re-framing inquiries regarding learning and unconventional computing with a fresh rationale for many-body physics out of equilibrium.

Interpretable Machine Learning in Physics: A Review

Machine learning is increasingly transforming various scientific fields, enabled by advancements in computational power and access to large data sets from experiments and simulations. As artificial intelligence (AI) continues to grow in capability, these algorithms will enable many scientific discoveries beyond human capabilities. Since the primary goal of science is to understand the world around us, fully leveraging machine learning in scientific discovery requires models that are interpretable -- allowing experts to comprehend the concepts underlying machine-learned predictions. Successful interpretations increase trust in black-box methods, help reduce errors, allow for the improvement of the underlying models, enhance human-AI collaboration, and ultimately enable fully automated scientific discoveries that remain understandable to human scientists. This review examines the role of interpretability in machine learning applied to physics. We categorize different aspects of interpretability, discuss machine learning models in terms of both interpretability and performance, and explore the philosophical implications of interpretability in scientific inquiry. Additionally, we highlight recent advances in interpretable machine learning across many subfields of physics. By bridging boundaries between disciplines -- each with its own unique insights and challenges -- we aim to establish interpretable machine learning as a core research focus in science.