Miriam Klopotek

Patrick Egenlauf, Iva Březinová, Sabine Andergassen et al.

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.

Sebastian Johann Wetzel, Seungwoong Ha, Raban Iten et al.

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.

Mario U. Gaimann, Miriam Klopotek

Information processing abilities of active matter are studied in the reservoir computing (RC) paradigm to infer the future state of a chaotic signal. We uncover an exceptional regime of agent dynamics that has been overlooked previously. It appears robustly optimal for performance under many conditions, thus providing valuable insights into computation with physical systems more generally. The key to forming effective mechanisms for information processing appears in the system's intrinsic relaxation abilities. These are probed without actually enforcing a specific inference goal. The dynamical regime that achieves optimal computation is located just below a critical damping threshold, involving a relaxation with multiple stages, and is readable at the single-particle level. At the many-body level, it yields substrates robustly optimal for RC across varying physical parameters and inference tasks. A system in this regime exhibits a strong diversity of dynamic mechanisms under highly fluctuating driving forces. Correlations of agent dynamics can express a tight relationship between the responding system and the fluctuating forces driving it. As this model 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.

Mario U. Gaimann, Miriam Klopotek

Reservoir computing (RC) is a state-of-the-art machine learning method that makes use of the power of dynamical systems (the reservoir) for real-time inference. When using biological complex systems as reservoir substrates, it serves as a testbed for basic questions about bio-inspired computation -- of how self-organization generates proper spatiotemporal patterning. Here, we use a simulation of an active matter system, driven by a chaotically moving input signal, as a reservoir. So far, it has been unclear whether such complex systems possess the capacity to process information efficiently and independently of the method by which it was introduced. We find that when switching from a repulsive to an attractive driving force, the system completely changes the way it computes, while the predictive performance landscapes remain nearly identical. The nonlinearity of the driver's injection force improves computation by decoupling the single-agent dynamics from that of the driver. Triggered are the (re-)growth, deformation, and active motion of smooth structural boundaries (interfaces), and the emergence of coherent gradients in speed -- features found in many soft materials and biological systems. The nonlinear driving force activates emergent regulatory mechanisms, which manifest enhanced morphological and dynamic diversity -- arguably improving fading memory, nonlinearity, expressivity, and thus, performance. We further perform RC in a broad variety of non-equilibrium active matter phases that arise when tuning internal (repulsive) forces for information transfer. Overall, we find that active matter agents forming liquid droplets are particularly well suited for RC. The consistently convex shape of the predictive performance landscapes, together with the observed phenomenological richness, conveys robustness and adaptivity.