Traditional physically-based material models rely on analytically derived bidirectional reflectance distribution functions (BRDFs), typically by considering statistics of micro-primitives such as facets, flakes, or spheres, sometimes combined with multi-bounce interactions such as layering and multiple scattering. These derivations are often complex and model-specific. Once an analytic BRDF evaluation is defined, one still needs to design an importance sampling method for it and evaluate the probability density function (pdf) of that sampling distribution, requiring further model-specific derivations. We present PureSample: a novel neural BRDF representation that allows learning a material’s appearance purely by sampling forward random walks on the microgeometry, which is usually straightforward to implement. Our representation allows for efficient BRDF evaluation, importance sampling, and pdf evaluation, for homogeneous as well as spatially varying materials. We achieve this by two learnable components: first, the sampling distribution is modeled using a flow matching neural network, which allows both importance sampling and pdf evaluation; second, we introduce a view-dependent albedo term, captured by a lightweight neural network, which allows for converting a pdf value to a BRDF value for any pair of view and light directions. We demonstrate PureSample on challenging materials, including various microgeometries, multi-layered materials, and multiple-scattering microfacet materials.
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Generative models for material creation are fundamentally limited by the quality and expressivity of available training data. Simple physically based rendering (PBR) materials, which combine a diffuse term with a single-lobe specular component, are commonly used for training but are insufficient to capture many important visual effects present in real materials. We present a method that enhances such simple PBR materials to more expressive ones, by augmenting the single GGX specular lobe into a layered model that captures a broader range of non-diffuse effects. Starting from a simple material, we procedurally construct a corresponding multi-lobe non-diffuse component guided by physical priors, enabling effects such as dust, clearcoat, and layered scattering. To provide a compact representation for downstream applications, we encode this non-diffuse component as a neural material with a shared 6D latent space, where each material instance is represented by two latent textures and decoded by a pretrained universal MLP. We further regularize the latent space to support material generation. The resulting neural material dataset enables training generative models for richer material creation. To demonstrate this application, we finetune a video diffusion model to produce neural latent textures that encode our multi-lobe material, and present generative results as proof of feasibility. Our procedural data enhancement approach is an important step toward improving expressivity in material generation.
Reconstructing dynamic fluids from sparse-view videos is a severely under-constrained problem due to complex volumetric visibility and turbulent, topology-changing motion. Current dynamic deformation-based 3D Gaussian Splatting (3DGS) methods use heuristic image-space warps, which often overfit limited observations via non-physical primitive scaling or drifting, producing floaters and geometric distortions. To address these challenges, we propose a hybrid, physics-aware fluid representation that injects physical constraints directly into the 3DGS pipeline. We develop a Beer–Lambert volumetric model mapping Gaussian primitives to a continuous, physically-grounded density field, bridging optical observations with fundamental physical laws. A physically-guided optimization evolves primitives under a global, volume-preserving velocity field, avoiding arbitrary per-particle deformations and effectively preserving volume while recovering fine-scale turbulent details. This unified formulation tightly couples fluid dynamics with differentiable rendering, enabling high-quality, joint predictions of velocity and density. Experiments on synthetic and real smoke datasets demonstrate that our approach surpasses state-of-the-art methods in both visual fidelity and physical consistency, achieving stable 3D reconstructions even from sparse views.
Eigenanalysis of partial differential operators is essential in reduced-order modeling for physical simulation, providing eigenmode representations in elasticity, acoustics, and transient heat transport. While recent neural, mesh-free, and geometry-agnostic approaches enable differentiable eigenanalysis over continuously parameterized shape spaces, boundary conditions of eigenfunctions are limited to Neumann-type (natural) conditions, hindering their applicability in scenarios where boundary conditions must be precisely controlled or optimized. In this work, we focus on Laplace-type operators and extend shape space neural eigenanalysis to handle boundary conditions beyond natural Neumann settings. Building on the same variational, energy-based formulation, we show that Dirichlet, Robin, and mixed boundary conditions can be incorporated without altering the underlying eigenvalue optimization principle. In our formulation, boundary configurations—including boundary placement and Robin coefficients modeling boundary exchange processes—are treated as first-class parameters rather than fixed constraints. When combined with shape-parameterized domains, this leads to a joint shape–boundary space formulation, allowing eigenfunctions and spectra to be evaluated consistently across variations in both geometry and boundary configuration. We conduct experiments on representative applications such as boundary-driven spectral optimization for rigid-walled cavity resonance tuning, reduced-order simulation with changing supports, and analysis of transient thermal behavior under varying boundary exchange conditions. By elevating boundary conditions from fixed constraints to operator-wise parameterization, our approach broadens the applicability of Laplace-type neural eigenanalysis to physical systems where boundary constraints serve as critical design and control variables.
Graph-based collaborative filtering has advanced by modeling higher-order interactions, yet performance remains constrained by underlying geometric assumptions and propagation schemes. User-item interaction graphs typically exhibit pronounced topological heterogeneity, whereas existing methods rely on a fixed, homogeneous geometry and employ tangent space aggregation. To address these fundamental limitations, this paper introduces Adaptive Geometric Collaborative Filtering (AGCF), a novel method rooted in Hamiltonian dynamics, which reframes representation learning as a physical process evolving on a time-varying manifold. AGCF is distinguished by an integrated design comprising: (1) a learnable, node-dependent Riemannian metric that construct a continuous heterogeneous manifold aligned with local topology; (2) unified dynamic trajectories that achieve intrinsic propagation without tangent space approximations; (3) a channel-wise metric that captures semantic anisotropy in the feature space. We rigorously prove global existence and uniqueness of the induced dynamics and explain the mechanism enabling long-range information propagation. Extensive experiments on five benchmark datasets show consistent gains over representative baselines.
Opinion propagation research primarily focuses on phenomenon prediction rather than mechanism understanding, lacking interpretable frameworks to reveal underlying propagation dynamics. This limitation stems from two sources: existing methods employ end-to-end paradigms where parameters lack physical meanings, while available datasets suffer from incomplete hierarchical structures, coarse sentiment annotations, and limited domain coverage. To address these limitations, we introduce VISTA, a multi-dimensional opinion propagation dataset providing complete hierarchical structures, fine-grained emotional annotations, and cross-domain coverage. Based on this dataset, we propose an interpretable modeling framework integrating high-dimensional Hawkes processes with graph neural networks, enabling parametric expression of propagation mechanisms through event space constructed from emotional and reply level combinations. Through interpretable parameter analysis, we reveal three mechanistic patterns: differential emotional propagation strength, asymmetric hierarchical excitation, and temporal memory effects. Our framework establishes quantitative foundations for understanding opinion propagation dynamics, achieving best performance in sentiment prediction and structural consistency tasks while providing the first benchmark for multi-dimensional propagation mechanism analysis.
In the literature, prior research on Security-oriented Video Understanding (SVU) has predominantly focused on detecting and locating the threats (e.g., shootings, robberies) in videos, while largely lacking the effective capability to generate and evaluate the threat causes. Motivated by these gaps, this paper introduces a new chat paradigm SVU task, i.e., In-depth Security-oriented Video Understanding (DeepSVU), which aims to not only identify and locate the threats but also attribute and evaluate the causes of threatening segments in detail. Furthermore, this paper reveals two key challenges in the proposed task: 1) how to effectively model the coarse-to-fine physical-world information (e.g., human behavior, object interactions and background context) to boost the DeepSVU task, and 2) how to adaptively trade off these factors. Addressing these challenges is crucial for improving VAD, especially for identifying, locating, and attributing anomalies. To tackle these challenges, this paper proposes a new Unified Physical-world Regularized MoE (UPRM) approach. Specifically, UPRM incorporates two key components: the Unified Physical-world Enhanced MoE (UPE) Block and the Physical-world Trade-off Regularizer (PTR), to address the above two challenges, respectively. Extensive experiments conduct on our DeepSVU instructions datasets (i.e., UCF-C instructions and CUVA instructions) demonstrate that UPRM outperforms several advanced Video-LLMs as well as non-LLM approaches. such information.These justify the importance of the coarse-to-fine physical-world information in the DeepSVU task and demonstrate the effectiveness of our UPRM in capturing such information.
Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. In this work, we introduce the Complex-Valued Stuart-Landau Graph Neural Network (SLGNN), a novel architecture grounded in Stuart-Landau oscillator dynamics. Stuart-Landau oscillators are canonical models of limit-cycle behavior near Hopf bifurcations, which are fundamental to synchronization theory and are widely used in e.g.\ neuroscience for mesoscopic brain modeling. Unlike harmonic oscillators and phase-only Kuramoto models, Stuart-Landau oscillators retain both amplitude and phase dynamics, enabling rich phenomena such as amplitude regulation and multistable synchronization. The proposed SLGNN generalizes existing phase-centric Kuramoto-based OGNNs by allowing node feature amplitudes to evolve dynamically according to Stuart-Landau dynamics, with explicit tunable hyperparameters (such as the Hopf-parameter and the coupling strength) providing additional control over the interplay between feature amplitudes and network structure. We conduct extensive experiments across node classification, graph classification, and graph regression tasks, demonstrating that SLGNN outperforms existing OGNNs and establishes a novel, expressive, and theoretically grounded framework for deep oscillatory architectures on graphs. The code and hyperparameters for SLGNN are available at https://github.com/kevvzhang/StuartLandauGNN
Social event detection (SED) enhances public awareness by clustering large-scale social messages and has been widely applied across diverse domains. While many existing frameworks adopt Graph Convolution Networks (GCN) as backbones and extend them with auxiliary modules to model complex message relationships, they rarely explore the deeper potential of GCN itself. Specifically, the core operation of GCN—smoothed feature aggregation—implicitly assumes that social information diffusion follows a single-pass and independent heat propagation process. However, real-world diffusion is inherently multi-wave and oscillatory, where different messages interact through reinforcement and interference, resembling the principle of wave–particle duality. To address this gap, we propose Physics-Inspired Graph Convolution Networks (PIGCN ), a novel model that unifies wave-based propagation and particle-like interactions. Specifically, PIGCN integrates a Helmholtz Graph Filter module to capture spectral wave propagation with oscillatory dynamics, and a Physical Interaction Force mechanism to adaptively adjust edge weights by attracting messages within the same event and repelling those across events. Building on PIGCN, we further incorporate a contextualized text encoder and timestamp encoding to form a comprehensive SED framework. Extensive experiments demonstrate that PIGCN effectively outperforms conventional GCN baselines and achieves superior performance across multiple SED datasets, establishing a new benchmark for balancing architectural simplicity with effectiveness. Our code can be found on GitHub . https://github.com/yuyongsheng1990/PIGCN
AI has reached a turning point. Systems can now perceive, generate, and act in language and image across digital platforms at unprecedented scale. Yet as AI moves from tools to collaborators—embedded in decision-making, institutions, and everyday life—a new requirement becomes unavoidable: AI must understand the world the way humans inhabit it. This talk introduces Cognitive World Modeling as the next phase of AI development. It unifies physical world modeling—time, space, causality, action—with mental world modeling—goals, beliefs, intentions, emotions, and social norms—into a single, persistent representation of reality as experienced by humans. Together, these models allow AI systems not only to predict outcomes, but to reason about meaning, context, and consequence. Cognitive World Modeling moves AI beyond reactive toward systems that can plan, explain, adapt, and collaborate over time. Alignment and trust emerge not as post hoc constraints, but as properties of systems that maintain accurate, evolving models of both the external world and the humans within it.
Machine learning models for steel property prediction routinely report high-quality metrics with R² > 0.85, yet these results rely on random splits that allow similar grades in both train and test sets. We present SteelAgent, an interactive system that exposes a critical generalization gap: the same models drop from R² > 0.85 to R² = 0.11 on unseen steel families, revealing more than 7 times higher quality degradation. Similarly, conformal prediction coverage degrades from 91% to 38% under distribution shift induced by holding out substantial data sources. SteelAgent combines physics-informed features grounded in classical metallurgy and interpretable models with conformal uncertainty quantification, and an LLM orchestrator that coordinates six domain-specific tools. The system supports property prediction with specification compliance checking, competitive steel comparison, and cost-aware inverse alloy design over 3,741 heat treatment records spanning 1,234 grades. All predictions are traceable through explicit tool calls, ensuring that all physical quantities are computed, not generated. We made the code and data freely accessible to the community.
Recent progress in Large Language Models (LLMs) has transformed text and code generation, yet models still falter on Partial Differential Equations (PDEs) where correctness, constraints, and physical consequences are critical. We explore how formal LLM reasoning can advance symbolic PDE modeling. First, our PDE-Controller formalizes informal PDEs, synthesizes solver-ready code, and plans subgoals to tackle nonconvex control via interactions with external solvers. Second, our Lean Finder accelerates PDE formalization via a semantics-aware search engine for Lean/Mathlib that retrieves relevant theorems, outperforming GPT models and gaining significant traction in the AI-for-math community. Through these efforts, we aim to design a semantics-first LLM that autoformalizes informal PDE problems into machine-checked specifications and synthesizes solver-ready code. This closes the loop between formal analysis and LLM reasoning, ultimately surpassing human heuristics across PDEs.
3D scene generation has rapidly evolved, significantly promoting the innovation of content creation. In this context, interaction techniques serve as a pivotal bridge connecting user intent with the generative models, thereby enabling precise control, real-time feedback and personalized customization of complex 3D scenes. Existing literature reviews predominantly focus on general generative paradigms, or are limited to specific subdomains such as single-object modeling, while often overlooking the systematic classification of interaction mechanisms. To bridge this gap, this work presented a comprehensive survey of interaction techniques in 3D scene generation. We proposed a unified taxonomy that categorized existing methods into three primary paradigms: Interactive Generation, Interactive Editing, and Embodied Interaction. For each category, we analyzed representative methods in terms of controllability, interaction granularity, and physical consistency, and discussed their advantages and limitations. We further summarized commonly used datasets and evaluation protocols for interactive 3D scene generation. Finally, we discussed the future directions toward more physically grounded, multi-modal, and user-centered interactive 3D scene generation systems. A curated list of the related papers mentioned in this work can be found at Awesome-Interactive-Techniques-in-3D-Scene-Generation-Lists.
Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on machine learning-based components. Despite the emergence of various physics-aware data-driven approaches, the field still lacks a unified perspective to uncover their relationships, limitations, and appropriate roles in scientific workflows. To this end, we propose a unifying perspective that places two dominant paradigms, Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs), within a shared design space. We organize existing methods from three fundamental dimensions: what is learned, how physical structures are integrated into the learning process, and how the computational load is amortized across problem instances. In this way, many practical challenges can be best understood as consequences of these structural properties of learning PDEs. By analyzing recent advances through this unifying view, our survey aims to facilitate the development of reliable learning-based PDE solvers and help catalyze a deeper synthesis of physics and data.
Recent progress in generalizable embodied control has been driven by large-scale pretraining of Vision–Language–Action (VLA) models. However, most existing approaches rely on large collections of robot demonstrations, which are costly to obtain and tightly coupled to specific embodiments. Human videos, by contrast, are abundant and capture rich interactions, providing diverse semantic and physical cues for real-world manipulation. Yet, embodiment differences and the frequent absence of task-aligned annotations make their direct use in VLA models challenging. This survey provides a unified view of how human videos are transformed into effective knowledge for VLA models. We categorize existing approaches into four classes based on the action-related information they derive: (i) latent action representations that encode inter-frame changes; (ii) predictive world models that forecast future frames; (iii) explicit 2D supervision that extracts image-plane cues; and (iv) explicit 3D reconstruction that recovers geometry or motion. Beyond this taxonomy, we highlight three key open challenges in this area: structuring unstructured videos into training-ready episodes, grounding video-derived supervision into robot-executable actions under embodiment and viewpoint heterogeneity, and designing evaluation protocols that better predict real-world deployment performance and transfer efficiency, thereby informing future research directions.
With the impressive progress of deep learning, applications relying on machine learning are increasingly being integrated into daily life. However, most deep learning models have an opaque, oracle-like nature making it difficult to interpret and understand their decisions. This problem led to the development of the field known as eXplainable Artificial Intelligence (XAI). One method in this field known as Projective Simulation (PS) models a chain-of-thought as a random walk of a particle on a graph with vertices that have concepts attached to them. While this description has various benefits, including the possibility of quantization, it cannot be naturally used to model thoughts that combine several concepts simultaneously. To overcome this limitation, we introduce Multi-Excitation Projective Simulation (mePS), a generalization that considers a chain-of-thought to be a random walk of several particles on a hypergraph. A definition for a dynamic hypergraph is put forward to describe the agent's training history along with applications to AI and hypergraph visualization. An inductive bias inspired by the remarkably successful few-body interaction models used in quantum many-body physics is formalized for our classical mePS framework and employed to tackle the exponential complexity associated with naive implementations of hypergraphs. We prove that our inductive bias reduces the complexity from exponential to polynomial, with the exponent representing the cutoff on how many particles can interact. We numerically apply our method to two toy environments and a more complex scenario modelling the diagnosis of a broken computer. These environments demonstrate the resource savings provided by an appropriate choice of inductive bias, as well as showcasing aspects of interpretability. A quantum model for mePS is also briefly outlined and some future directions for it are discussed.
Large Language Models (LLMs) can generate Computer-Aided Design (CAD), yet lack physical comprehension required for reliable engineering design. Instead of attempting to implicitly learn physical laws from data, we propose a Hybrid Agentic-Physical Architecture that embeds validated knowledge-based engineering tools directly into the decision-making loop of autonomous AI agents. In this framework, engineering design is formulated as a closed-loop, sequential decision-making process guided by explicit physical verification. Based on a load case, dedicated agents iteratively plan, generate, evaluate, and revise engineering designs using knowledge-based tools as a feedback signal. We introduce a benchmark dataset and metrics for assessing functional validity in generative CAD. Our system generates more complex and physically verified designs, with a 4.2x increase in structural complexity and improving compile rate by 3.5% compared to similar agentic methods. The codebase, prompts and dataset will be made publicly available to support reproducibility and future research.
Macro placement is a pivotal stage in VLSI physical design, fundamentally determining the overall chip performance. Recent data-driven placement methods have demonstrated significant potential, yet they often struggle to handle sequential dependencies and to balance topological connectivity with physical constraints. To bridge this gap, we propose MacroDiff+, a physics-guided geometric diffusion framework. Specifically, we design a dual-domain denoising architecture that couples topological connectivity encoded by heterogeneous GNNs with global geometric context modeled by a Transformer. Furthermore, we introduce Physics-Guided Sampling, an inference strategy that actively steers the generation using explicit gradients to ensure both statistical plausibility and physical validity. On the ISPD2005 MMS benchmarks, MacroDiff+ outperforms state-of-the-art baselines with a 6.1–6.2% reduction in wirelength. Notably, it exhibits superior stability and scalability on large-scale designs where prior methods fail to converge. The source code is provided at https://github.com/jhy00n/MacroDiff-plus.
Meteorological downscaling is crucial for high-resolution regional climate forecasting and disaster early warning. While neural operators have emerged as a promising paradigm for modeling complex spatiotemporal mappings, existing frameworks often struggle with spherical manifold geometric distortions, inherent atmospheric multi-scale coupling mismatches, and lack of explicit atmospheric laws. We propose the Spherical Physics-informed Neural Operator, which utilizes a Spherical Laplacian Decomposition to partition atmospheric fields into hierarchical frequency components, maintaining exact point-wise correspondence across scales. To evaluate these representations at arbitrary locations, we introduce a localized spherical integral operator that approximates continuous kernel transforms via geometry-aware attention. Dynamical consistency is further enforced by embedding differentiable constraints into the learning process. Extensive experiments demonstrate that our framework attains superior accuracy and zero-shot generalization across various meteorological variables and unseen queries, representing a robust and interpretable solution for global-to-regional meteorological downscaling.
Flood models inform strategic disaster management by simulating the spatiotemporal hydrodynamics of flooding. While physics-based numerical flood models are accurate, their substantial computational cost limits their use in operational settings where rapid predictions are essential. Models designed with graph neural networks (GNNs) provide both speed and accuracy while having the ability to process unstructured spatial domains. Given its flexible input and architecture, GNNs can be leveraged alongside physics-informed techniques with ease, significantly improving interpretability and generalizability. We introduce a novel flood GNN architecture, DUALFloodGNN, which embeds physical constraints at both global and local scales through explicit loss terms. The model jointly predicts water volume at nodes and flow along edges through a shared message-passing framework. To improve performance for autoregressive inference, model training is conducted with a multi-step loss enhanced with dynamic curriculum learning. Compared with standard GNN architectures and state-of-the-art GNN flood models, DUALFloodGNN achieves substantial improvements in predicting multiple hydrologic variables (e.g., water volume, flow, and depth) while maintaining high computational efficiency. The model is open sourced at https://github.com/acostacos/dual_flood_gnn. The dataset is open sourced at https://doi.org/10.25910/9xav-0s86.