Physics-Informed Modeling and Control of Emergent Behaviors in Robot Swarms

Robot swarms can exhibit coherent collective behaviors through local perception, limited communication and decentralized decision-making, yet modeling and controlling such emergence remains challenging when behaviors unfold over multiple phases. Here we introduce PhySwarm, a physics-informed micro--macro framework that represents multi-stage swarm emergence as physically constrained density-field evolution coupled to executable robot motion. At the macroscopic level, a multi-phase advection--diffusion--reaction model (Macro-ADR) describes phase-dependent swarm-density evolution through directed transport, diffusion-based spatial regulation and behavioral phase transitions. At the microscopic level, an equivalent deterministic motion model (Micro-EDM) realizes these mechanisms through potential-field advection, density-gradient compensation and rate- or event-gated phase switching. A neural-physics controller (NPC) maps local observations and temporal memory to bounded physical parameters, and is trained with a reinforcement learning--PINN objective that combines task rewards with macro-scale density residuals and micro-scale motion-consistency constraints. In several proof-of-concept swarm missions -- including trail-guided foraging, formation-reconfigurable navigation and role-adaptive search and rescue -- we demonstrate that PhySwarm can generate distinct multi-stage emergent behaviors within a unified physics-informed modeling framework. The learned density fields and physical parameters provide interpretable evidence of how advection, diffusion and reaction jointly regulate multi-stage swarm organization. These results establish a physics-informed route for learning, interpreting and controlling emergent behaviors in robot swarms.

Causal Interpretable Progression Trajectory Analysis of Chronic Disease

Chronic disease is the leading cause of death, emphasizing the need for accurate prediction of disease progression trajectories and informed clinical decision-making. Machine learning (ML) models have shown promise in this domain by capturing non-linear patterns within patient features. However, existing ML-based models lack the ability to provide causal interpretable predictions and estimate treatment effects, limiting their decision-assisting perspective. In this study, we propose a novel model called causal trajectory prediction (CTP) to tackle the limitation. The CTP model combines trajectory prediction and causal discovery to enable accurate prediction of disease progression trajectories and uncovering causal relationships between features. By incorporating a causal graph into the prediction process, CTP ensures that ancestor features are not influenced by treatment on descendant features, thereby enhancing the interpretability of the model. By estimating the bounds of treatment effects, even in the presence of unmeasured confounders, the CTP provides valuable insights for clinical decision-making. We evaluate the performance of the CTP using simulated and real medical datasets. Experimental results demonstrate that our model achieves satisfactory performance, highlighting its potential to assist clinical decisions.