Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of tumor cells within a patient's anatomy. While medical imaging can detect the bulk of a tumor, it cannot capture the full extent of its spread, as low-concentration tumor cells often remain undetectable, particularly in glioblastoma, the most common primary brain tumor. Machine learning approaches struggle to estimate the complete tumor cell distribution due to a lack of appropriate training data. Consequently, most existing methods rely on physics-based simulations to generate anatomically and physiologically plausible estimations. However, these approaches face challenges with complex and unknown initial conditions and are constrained by overly rigid physical models.

The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs) from data poses significant challenges, primarily in determining relevant terms from a vast search space. Symmetry, as a crucial prior knowledge in scientific fields, has been widely applied in tasks such as designing equivariant networks and guiding neural PDE solvers. In this paper, we propose a pipeline for governing equation discovery based on differential invariants, which can losslessly reduce the search space of existing equation discovery methods while strictly adhering to symmetry. Specifically, we compute the set of differential invariants corresponding to the infinitesimal generators of the symmetry group and select them as the relevant terms for equation discovery. Taking DI-SINDy (SINDy based on Differential Invariants) as an example, we demonstrate that its success rate and accuracy in PDE discovery surpass those of other symmetry-informed governing equation discovery methods across a series of PDEs.

--Data centers are the backbone of computing capacity. Operating data centers in the tropical regions faces unique challenges due to consistently high ambient temperature and elevated relative humidity throughout the year . These conditions result in increased cooling costs to maintain the reliability of the computing systems. While existing machine learning-based approaches have demonstrated potential to elevate operations to a more proactive and intelligent level, their deployment remains dubious due to concerns about model extrapolation capabilities and associated system safety issues. T o address these concerns, this article proposes incorporating the physical characteristics of data centers into traditional data-driven machine learning solutions. We begin by introducing the data center system, including the relevant multiphysics processes and the data-physics availability. Next, we outline the associated modeling and optimization problems and propose an integrated, physics-informed machine learning system to address them. Using the proposed system, we present relevant applications across varying levels of operational intelligence. A case study on an industry-grade tropical data center is provided to demonstrate the effectiveness of our approach. Finally, we discuss key challenges and highlight potential future directions. He data center (DC) industry is experiencing rapid growth driven by the increasing demand for cloud computing, data storage, and artificial intelligence (AI) services. This expansion is also occurring in tropical regions, where digital infrastructure is being scaled up to meet regional computing needs [1]. As DCs grow in size and complexity, their power consumption increases accordingly, particularly in tropical climates where high ambient temperature and humidity place additional strain on the cooling systems. According to the International Energy Agency (IEA), global DC energy consumption could rise to 1050 TWh by 2026, up from 460 TWh in 2022 [2].

Large Language Models (LLMs) have shown state-of-the-art performance in a variety of tasks, including arithmetic and reasoning; however, to gauge the intellectual capabilities of LLMs, causal reasoning has become a reliable proxy for validating a general understanding of the mechanics and intricacies of the world similar to humans. Previous works in natural language processing (NLP) have either focused on open-ended causal reasoning via causal commonsense reasoning (CCR) or framed a symbolic representation-based question answering for theoretically backed-up analysis via a causal inference engine. The former adds an advantage of real-world grounding but lacks theoretically backed-up analysis/validation, whereas the latter is far from real-world grounding. In this work, we bridge this gap by proposing the COLD (Causal reasOning in cLosed Daily activities) framework, which is built upon human understanding of daily real-world activities to reason about the causal nature of events. We show that the proposed framework facilitates the creation of enormous causal queries ( 9 million) and comes close to the mini-turing test, simulating causal reasoning to evaluate the understanding of a daily real-world task.

Existing protein-ligand docking studies typically focus on the self-docking scenario, which is less practical in real applications. Moreover, some studies involve heavy frameworks requiring extensive training, posing challenges for convenient and efficient assessment of docking methods. To fill these gaps, we design PoseX, an open-source benchmark to evaluate both self-docking and cross-docking, enabling a practical and comprehensive assessment of algorithmic advances. Specifically, we curated a novel dataset comprising 718 entries for self-docking and 1,312 entries for cross-docking; second, we incorporated 23 docking methods in three methodological categories, including physics-based methods (e.g., Schrödinger Glide), AI docking methods (e.g., DiffDock) and AI co-folding methods (e.g., AlphaFold3); third, we developed a relaxation method for post-processing to minimize conformational energy and refine binding poses; fourth, we built a leaderboard to rank submitted models in real-time. We derived some key insights and conclusions from extensive experiments: (1) AI approaches have consistently outperformed physics-based methods in overall docking success rate. (2) Most intra- and intermolecular clashes of AI approaches can be greatly alleviated with relaxation, which means combining AI modeling with physics-based post-processing could achieve excellent performance. (3) AI co-folding methods exhibit ligand chirality issues, except for Boltz-1x, which introduced physics-inspired potentials to fix hallucinations, suggesting modeling on stereochemistry improves the structural plausibility markedly. (4) Specifying binding pockets significantly promotes docking performance, indicating that pocket information can be leveraged adequately, particularly for AI co-folding methods, in future modeling efforts. The code, dataset, and leaderboard are released at https://github.com/CataAI/PoseX.

Graph-structured data pervades domains such as social networks, biological systems, knowledge graphs, and recommender systems. While foundation models have transformed natural language processing, vision, and multimodal learning through large-scale pretraining and generalization, extending these capabilities to graphs -- characterized by non-Euclidean structures and complex relational semantics -- poses unique challenges and opens new opportunities. To this end, Graph Foundation Models (GFMs) aim to bring scalable, general-purpose intelligence to structured data, enabling broad transfer across graph-centric tasks and domains. This survey provides a comprehensive overview of GFMs, unifying diverse efforts under a modular framework comprising three key components: backbone architectures, pretraining strategies, and adaptation mechanisms. We categorize GFMs by their generalization scope -- universal, task-specific, and domain-specific -- and review representative methods, key innovations, and theoretical insights within each category. Beyond methodology, we examine theoretical foundations including transferability and emergent capabilities, and highlight key challenges such as structural alignment, heterogeneity, scalability, and evaluation. Positioned at the intersection of graph learning and general-purpose AI, GFMs are poised to become foundational infrastructure for open-ended reasoning over structured data. This survey consolidates current progress and outlines future directions to guide research in this rapidly evolving field. Resources are available at https://github.com/Zehong-Wang/Awesome-Foundation-Models-on-Graphs.

Humans excel in navigating diverse, complex environments with agile motor skills, exemplified by parkour practitioners performing dynamic maneuvers, such as climbing up walls and jumping across gaps. Reproducing these agile movements with simulated characters remains challenging, in part due to the scarcity of motion capture data for agile terrain traversal behaviors and the high cost of acquiring such data. In this work, we introduce PARC (Physics-based Augmentation with Reinforcement Learning for Character Controllers), a framework that leverages machine learning and physics-based simulation to iteratively augment motion datasets and expand the capabilities of terrain traversal controllers. PARC begins by training a motion generator on a small dataset consisting of core terrain traversal skills. The motion generator is then used to produce synthetic data for traversing new terrains. However, these generated motions often exhibit artifacts, such as incorrect contacts or discontinuities. To correct these artifacts, we train a physics-based tracking controller to imitate the motions in simulation. The corrected motions are then added to the dataset, which is used to continue training the motion generator in the next iteration. PARC's iterative process jointly expands the capabilities of the motion generator and tracker, creating agile and versatile models for interacting with complex environments. PARC provides an effective approach to develop controllers for agile terrain traversal, which bridges the gap between the scarcity of motion data and the need for versatile character controllers.

We propose PhysicsFC, a method for controlling physically simulated football player characters to perform a variety of football skills--such as dribbling, trapping, moving, and kicking--based on user input, while seamlessly transitioning between these skills. Our skill-specific policies, which generate latent variables for each football skill, are trained using an existing physics-based motion embedding model that serves as a foundation for reproducing football motions. Key features include a tailored reward design for the Dribble policy, a two-phase reward structure combined with projectile dynamics-based initialization for the Trap policy, and a Data-Embedded Goal-Conditioned Latent Guidance (DEGCL) method for the Move policy. Using the trained skill policies, the proposed football player finite state machine (PhysicsFC FSM) allows users to interactively control the character. To ensure smooth and agile transitions between skill policies, as defined in the FSM, we introduce the Skill Transition-Based Initialization (STI), which is applied during the training of each skill policy. We develop several interactive scenarios to showcase PhysicsFC's effectiveness, including competitive trapping and dribbling, give-and-go plays, and 11v11 football games, where multiple PhysicsFC agents produce natural and controllable physics-based football player behaviors. Quantitative evaluations further validate the performance of individual skill policies and the transitions between them, using the presented metrics and experimental designs.

Material stress analysis is a critical aspect of material design and performance optimization. Under dynamic loading, the global stress evolution in materials exhibits complex spatiotemporal characteristics, especially in two-phase random materials (TRMs). Such kind of material failure is often associated with stress concentration, and the phase boundaries are key locations where stress concentration occurs. In practical engineering applications, the spatiotemporal resolution of acquired microstructural data and its dynamic stress evolution is often limited. This poses challenges for deep learning methods in generating high-resolution spatiotemporal stress fields, particularly for accurately capturing stress concentration regions. In this study, we propose a framework for global stress generation and spatiotemporal super-resolution in TRMs under dynamic loading. First, we introduce a diffusion model-based approach, named as Spatiotemporal Stress Diffusion (STS-diffusion), for generating global spatiotemporal stress data. This framework incorporates Space-Time U-Net (STU-net), and we systematically investigate the impact of different attention positions on model accuracy. Next, we develop a physics-informed network for spatiotemporal super-resolution, termed as Spatiotemporal Super-Resolution Physics-Informed Operator (ST-SRPINN). The proposed ST-SRPINN is an unsupervised learning method. The influence of data-driven and physics-informed loss function weights on model accuracy is explored in detail. Benefiting from physics-based constraints, ST-SRPINN requires only low-resolution stress field data during training and can upscale the spatiotemporal resolution of stress fields to arbitrary magnifications.

Combining physics-based modeling with data-driven methods is critical to enabling the translation of computational methods to clinical use in cardiology. The use of rigorous differential equations combined with machine learning tools allows for model personalization with uncertainty quantification in time frames compatible with clinical practice. However, accurate and efficient surrogate models of cardiac function, built from physics-based numerical simulation, are still mostly geometry-specific and require retraining for different patients and pathological conditions. We propose a novel computational pipeline to embed cardiac anatomies into full-field surrogate models. We generate a dataset of electrophysiology simulations using a complex multi-scale mathematical model coupling partial and ordinary differential equations. We adopt Branched Latent Neural Maps (BLNMs) as an effective scientific machine learning method to encode activation maps extracted from physics-based numerical simulations into a neural network. Leveraging large deformation diffeomorphic metric mappings, we build a biventricular anatomical atlas and parametrize the anatomical variability of a small and challenging cohort of 13 pediatric patients affected by Tetralogy of Fallot. We propose a novel statistical shape modeling based z-score sampling approach to generate a new synthetic cohort of 52 biventricular geometries that are compatible with the original geometrical variability. This synthetic cohort acts as the training set for BLNMs. Our surrogate model demonstrates robustness and great generalization across the complex original patient cohort, achieving an average adimensional mean squared error of 0.0034. The Python implementation of our BLNM model is publicly available under MIT License at https://github.com/StanfordCBCL/BLNM.