Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to discretisation, while canonical deep learning methods are data-hungry and struggle with chaotic dynamics and long-term predictions. Physics-Informed Neural Networks (PINNs) mitigate some of these issues by incorporating physical constraints in the learning process, yet they remain limited by mesh resolution and long-term predictive stability. In this work, we propose a Physics-Informed Neural Operator (PINO) approach to solve PDE problems in cardiac EP. Unlike PINNs, PINO models learn mappings between function spaces, allowing them to generalise to multiple mesh resolutions and initial conditions. Our results show that PINO models can accurately reproduce cardiac EP dynamics over extended time horizons and across multiple propagation scenarios, including zero-shot evaluations on scenarios unseen during training. Additionally, our PINO models maintain high predictive quality in long roll-outs (where predictions are recursively fed back as inputs), and can scale their predictive resolution by up to 10x the training resolution. These advantages come with a significant reduction in simulation time compared to numerical PDE solvers, highlighting the potential of PINO-based approaches for efficient and scalable cardiac EP simulations.

We introduce PhysWorld, a framework that enables robot learning from video generation through physical world modeling. Recent video generation models can synthesize photorealistic visual demonstrations from language commands and images, offering a powerful yet underexplored source of training signals for robotics. However, directly retargeting pixel motions from generated videos to robots neglects physics, often resulting in inaccurate manipulations. PhysWorld addresses this limitation by coupling video generation with physical world reconstruction. Given a single image and a task command, our method generates task-conditioned videos and reconstructs the underlying physical world from the videos, and the generated video motions are grounded into physically accurate actions through object-centric residual reinforcement learning with the physical world model. This synergy transforms implicit visual guidance into physically executable robotic trajectories, eliminating the need for real robot data collection and enabling zero-shot generalizable robotic manipulation. Experiments on diverse real-world tasks demonstrate that PhysWorld substantially improves manipulation accuracy compared to previous approaches. Visit \href{https://pointscoder.github.io/PhysWorld_Web/}{the project webpage} for details.

The convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with physical constraints, resulting in models that are accurate, mechanistic, generalizable, and able to extrapolate beyond observed domains. This review surveys recent advances in physics-informed neural networks and operator learning, differentiable molecular simulation, and hybrid physics-ML potentials, with emphasis on long-timescale kinetics, rare events, and free-energy estimation. We frame these approaches as solutions to the "biomolecular closure problem", recovering unresolved interactions beyond classical force fields while preserving thermodynamic consistency and mechanistic interpretability. We examine theoretical foundations, tools and frameworks, computational trade-offs, and unresolved issues, including model expressiveness and stability. We outline prospective research avenues at the intersection of machine learning, statistical physics, and computational chemistry, contending that future advancements will depend on mechanistic inductive biases, and integrated differentiable physical learning frameworks for biomolecular simulation and discovery.

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or discontinuous. Existing deep learning approaches either require extensive labeled datasets or are limited to specific measurement types, often leading to failure in such regimes and restricting their practical applicability. Here, a novel generative neural operator framework, IGNO, is introduced to overcome these limitations. IGNO unifies the solution of inverse problems from both point measurements and operator-valued data without labeled training pairs. This framework encodes high-dimensional, potentially discontinuous coefficient fields into a low-dimensional latent space, which drives neural operator decoders to reconstruct both coefficients and PDE solutions. Training relies purely on physics constraints through PDE residuals, while inversion proceeds via efficient gradient-based optimization in latent space, accelerated by an a priori normalizing flow model. Across a diverse set of challenging inverse problems, including recovery of discontinuous coefficients from solution-based measurements and the EIT problem with operator-based measurements, IGNO consistently achieves accurate, stable, and scalable inversion even under severe noise. It consistently outperforms the state-of-the-art method under varying noise levels and demonstrates strong generalization to out-of-distribution targets. These results establish IGNO as a unified and powerful framework for tackling challenging inverse problems across computational science domains.

Physics-Informed Machine Learning (PIML) has successfully integrated mechanistic understanding into machine learning, particularly in domains governed by well-known physical laws. This success has motivated efforts to apply PIML to biology, a field rich in dynamical systems but shaped by different constraints. Biological modeling, however, presents unique challenges: multi-faceted and uncertain prior knowledge, heterogeneous and noisy data, partial observability, and complex, high-dimensional networks. In this position paper, we argue that these challenges should not be seen as obstacles to PIML, but as catalysts for its evolution. We propose Biology-Informed Machine Learning (BIML): a principled extension of PIML that retains its structural grounding while adapting to the practical realities of biology. Rather than replacing PIML, BIML retools its methods to operate under softer, probabilistic forms of prior knowledge. We outline four foundational pillars as a roadmap for this transition: uncertainty quantification, contextualization, constrained latent structure inference, and scalability. Foundation Models and Large Language Models will be key enablers, bridging human expertise with computational modeling. We conclude with concrete recommendations to build the BIML ecosystem and channel PIML-inspired innovation toward challenges of high scientific and societal relevance.

Humanoid robots are promising to acquire various skills by imitating human behaviors. However, existing algorithms are only capable of tracking smooth, low-speed human motions, even with delicate reward and curriculum design. This paper presents a physics-based humanoid control framework, aiming to master highly-dynamic human behaviors such as Kungfu and dancing through multi-steps motion processing and adaptive motion tracking. For motion processing, we design a pipeline to extract, filter out, correct, and retarget motions, while ensuring compliance with physical constraints to the maximum extent. For motion imitation, we formulate a bi-level optimization problem to dynamically adjust the tracking accuracy tolerance based on the current tracking error, creating an adaptive curriculum mechanism. We further construct an asymmetric actor-critic framework for policy training. In experiments, we train whole-body control policies to imitate a set of highly-dynamic motions. Our method achieves significantly lower tracking errors than existing approaches and is successfully deployed on the Unitree G1 robot, demonstrating stable and expressive behaviors. The project page is https://kungfu-bot.github.io.

Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh-Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers' escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, while requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems.

The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal control system design. However, numerical solutions to this equation are computationally intensive, and analytical solutions are frequently unavailable. Knowledge-guided machine learning methodologies, such as physics-informed neural networks (PINNs), offer new alternative approaches that can alleviate the difficulties of solving the HJB equation numerically. This work presents a multistage ensemble framework to learn the optimal cost-to-go, and subsequently the corresponding optimal control signal, through the HJB equation. Prior PINN-based approaches rely on a stabilizing the HJB enforcement during training. Our framework does not use stabilizer terms and offers a means of controlling the nonlinear system, via either a singular learned control signal or an ensemble control signal policy. Success is demonstrated in closed-loop control, using both ensemble- and singular-control, of a steady-state time-invariant two-state continuous nonlinear system with an infinite time horizon, accounting of noisy, perturbed system states and varying initial conditions.

Recent advances in sensing and imaging technologies have enabled the collection of high-dimensional spatiotemporal data across complex geometric domains. However, effective modeling of such data remains challenging due to irregular spatial structures, rapid temporal dynamics, and the need to jointly predict multiple interrelated physical variables. This paper presents a physics-augmented multi-task Gaussian Process (P-M-GP) framework tailored for spatiotemporal dynamic systems. Specifically, we develop a geometry-aware, multi-task Gaussian Process (M-GP) model to effectively capture intrinsic spatiotemporal structure and inter-task dependencies. To further enhance the model fidelity and robustness, we incorporate governing physical laws through a physics-based regularization scheme, thereby constraining predictions to be consistent with governing dynamical principles. We validate the proposed P-M-GP framework on a 3D cardiac electrodynamics modeling task. Numerical experiments demonstrate that our method significantly improves prediction accuracy over existing methods by effectively incorporating domain-specific physical constraints and geometric prior.

Efficient exploration and mapping in unknown indoor environments is a fundamental challenge, with high stakes in time-critical settings. In current systems, robot perception remains confined to line-of-sight; occluded regions remain unknown until physically traversed, leading to inefficient exploration when layouts deviate from prior assumptions. In this work, we bring non-line-of-sight (NLOS) sensing to robotic exploration. We leverage single-photon LiDARs, which capture time-of-flight histograms that encode the presence of hidden objects - allowing robots to look around blind corners. Recent single-photon LiDARs have become practical and portable, enabling deployment beyond controlled lab settings. Prior NLOS works target 3D reconstruction in static, lab-based scenarios, and initial efforts toward NLOS-aided navigation consider simplified geometries. We introduce SuperEx, a framework that integrates NLOS sensing directly into the mapping-exploration loop. SuperEx augments global map prediction with beyond-line-of-sight cues by (i) carving empty NLOS regions from timing histograms and (ii) reconstructing occupied structure via a two-step physics-based and data-driven approach that leverages structural regularities. Evaluations on complex simulated maps and the real-world KTH Floorplan dataset show a 12% gain in mapping accuracy under < 30% coverage and improved exploration efficiency compared to line-of-sight baselines, opening a path to reliable mapping beyond direct visibility.