Spline-Based Boundary Representations for Sparse View Reconstruction and Simulation Using Isogeometric Analysis

Image-based reconstruction aims to recover three-dimensional geometry from images. Recent advances have enabled the recovery of visually detailed models, yet their representations are not well-suited for numerical simulation. Simulation frameworks typically require explicit, watertight, and smooth geometries to ensure numerical robustness and accuracy, properties that surfaces extracted from image-based reconstructions lack. We propose FORGE-SIM, a method to directly reconstruct a multi-patch B-spline boundary representation from sparse posed RGB images without manual intervention. By optimizing the spline representation itself, our approach produces compact, smooth, and watertight geometries that are natively compatible with both Computer Aided Design and simulation workflows. Additionally, we introduce a strategy to project observation-derived fields, such as a thermal state and semantic information, onto the reconstructed models in the same spline basis, enabling immediate use in simulation. We demonstrate that the obtained models are of sufficiently high quality to enable thermal simulation and modal analysis. By unifying image-based reconstruction and simulation-ready modeling within a single optimization framework, this work removes a long-standing barrier between computer vision and numerical analysis. We anticipate that it will enable new workflows for simulation-driven design, inspection, and digital twin applications.

Agentic Root Cause Analysis through Evidence-Grounded Reasoning

Diagnosing the root cause of anomalies is essential for safe industrial operation. Despite extensive sensor instrumentation, formulating hypotheses and gathering evidence remains a manual process, creating a major operational bottleneck. While existing data-driven approaches aim to automate this, two critical limitations restrict their deployment: their operate as black boxes unable to justify their diagnosis, and they require scarce labeled examples of faulty operation. To address this gap, we introduce AgentRCA, a zero-shot agentic framework for evidence-grounded root cause analysis. Rather than learning fault-specific mappings, AgentRCA performs inference-time reasoning by combining a data-driven digital twin (modeling normal system dynamics) with a tool-augmented large language model. The agent iteratively gathers statistical evidence, evaluates competing hypotheses, and identifies the physical fault that best explains the observed behavior. Evaluated on a real-world multiphase-flow facility and a large-scale chemical plant, AgentRCA achieves diagnostic performance competitive with fully supervised baselines without relying on fault-specific training. Crucially, it produces transparent reasoning traces that explicitly link observed symptoms to their underlying physical causes. These results establish autonomous hypothesis-driven reasoning as a practical foundation for scalable industrial root cause analysis.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise

Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training. To address these limitations, we propose Neural Kolmogorov Equations (NKEs), a deterministic, infinite-dimensional reformulation of Neural SDEs based on the Kolmogorov Forward equation, transforming the learning problem from modelling individual stochastic trajectories to modelling the evolution of probability densities. NKEs learn general Lévy-type stochastic forcing directly through the operator structure of the KFE, and enable parallel-in-time training via a Lagrangian Galerkin projection and operator splitting. We evaluate NKEs on several stochastic benchmarks, including systems with coupled noise and jump processes, and verify that NKEs provide flexible models that accurately recover deterministic and stochastic dynamics with competitive predictive accuracy and improved training efficiency. Code and pretrained models will be released.

Beyond Thermal Imaging: Inferring Thermophysical Properties from Time-Resolved Thermal Observations

Inferring latent physical properties from sensory observations is a fundamental challenge in machine perception. Among available sensing modalities, thermal imaging is particularly promising because temperature evolution is directly governed by heat-transfer physics and therefore encodes information about underlying thermophysical properties of a scene. Recovering spatially resolved thermophysical properties from thermal observations could transform applications ranging from digital twins and infrastructure monitoring to robotics and scientific imaging. However, existing thermal scene reconstruction methods can recover temperature fields in complex 3D environments without identifying the thermophyiscal properties that govern thermal evolution, whereas inverse methods provide physically interpretable parameter estimation but typically rely on simplified geometries and controlled experimental conditions. Here we introduce ThermoField, a framework that unifies thermal scene reconstruction and thermophysical parameter estimation through differentiable heat-transfer simulation. The proposed framework represents these quantities as spatially varying neural fields and constrains them through scene geometry, governing heat-transfer physics, and temporal thermal observations. We demonstrate that ThermoField jointly reconstructs geometry, estimates spatially varying thermal diffusivity, and predicts thermal evolution under previously unseen environmental conditions. By integrating neural scene representations with differentiable heat-transfer solver, the framework enables physically interpretable parameter inference in complex 3D scenes. Our results establish a bridge between thermal scene reconstruction and inverse heat-transfer analysis, providing a unified approach for geometry reconstruction, thermophysical property estimation, and predictive thermal simulation from thermal observations.

Relational and Sequential Conformal Inference for Energy Time Series over Graphs via Foundation Models

Accurate energy demand forecasting is essential for the reliable operation and planning of modern sustainable energy systems. Spatial-temporal graph neural networks (STGNNs) have recently achieved strong performance in point forecasting by jointly modeling temporal dynamics and relational dependencies across interconnected energy nodes. However, in real-world energy systems, accurate point forecasts alone are insufficient, as operators also require reliable uncertainty estimates to support risk-aware decision-making, grid stability, and operational planning under uncertainty. Conformal prediction provides a principled and model-agnostic framework for uncertainty quantification with statistical coverage guarantees, making it particularly attractive for safety-critical energy applications. However, existing conformal prediction approaches often fail to fully capture the complex spatial-temporal structure of energy systems. To address these limitations, we propose STOIC (Spatial-Temporal Graph Conformal Prediction with In-Context Learning), a novel framework that integrates graph-based forecasting with the zero-shot calibration capabilities of tabular foundation models. STOIC first generates point forecasts using an STGNN and subsequently reformulates spatial-temporal residuals into a tabular representation suitable for in-context learning. Leveraging a tabular foundation model, STOIC calibrates prediction intervals without task-specific retraining, effectively capturing both sequential and relational dependencies. We evaluate STOIC on five diverse benchmarks, including synthetic simulations as well as real-world electricity and district heating networks. Across all datasets, STOIC consistently outperforms existing conformal prediction baselines, delivering more reliable and robust uncertainty estimates for complex graph-structured energy time series.

Rethinking Object-Centric Representations for Video Dynamics Modeling

Unsupervised video object tracking aims to decompose dynamic scenes into persistent, object-centric entities without manual annotations. Many recent approaches rely on slot-based representations, where a fixed set of latent variables ("slots") represent individual objects across frames. To preserve object identity, these models enforce temporal consistency on slot embeddings. However, when appearance and pose are entangled, this consistency objective conflicts with object motion and viewpoint changes. As a result, slots tend to lock onto static regions (e.g., background) to satisfy the consistency objective, while foreground objects become fragmented across multiple slots or frequently swap identities. To address these limitations, we propose STAITUS, a unified framework that explicitly disentangles each slot into appearance and geometric pose (position/scale). Leveraging this disentanglement, STAITUS enforces within-frame spatial separation and applies temporal alignment only in appearance space, yielding sharper masks and more persistent identities under motion, occlusion, and object entry/exit. Furthermore, to mitigate over-segmentation, we introduce an adaptive gating mechanism that dynamically adjusts the number of active slots to match scene complexity. Extensive experiments on synthetic and real-world benchmarks demonstrate that STAITUS substantially outperforms state-of-the-art baselines in segmentation quality and tracking stability.

A Data-Free Symbolic Regression Approach for Solving Equations

Many equations arising in science currently cannot be solved by available analytical techniques and are therefore solved numerically, without yielding explicit symbolic expressions. Existing symbolic regression approaches can recover symbolic expressions, but require training data obtained from the underlying process, rather than the governing equation alone. We propose the Symbolic Equation Solver (SES), a framework that formulates equation solving as an optimization problem over differentiable symbolic models. SES constructs its objective from the equation together with initial or boundary conditions, eliminating the need for paired input-output data. The learned model is expressed in explicit symbolic form, enabling further analysis. We evaluate SES on representative algebraic and differential equations, including a system of algebraic equations, an equation with transcendental terms, an ordinary differential equation, and partial differential equations with different initial or boundary conditions. Across these settings, SES recovers compact symbolic expressions that match the corresponding analytical solutions.

Spatiotemporal Imputation with Graph-Informed Flow Matching

Missing data is a common challenge in spatiotemporal systems, arising in applications such as air quality monitoring and urban traffic management. Traditional machine learning approaches, like recurrent and graph neural networks, rely on iterative propagation, which tends to accumulate errors over time and space. Recent diffusion-based methods mitigate error propagation but require iterative sampling and often depend on problem-agnostic Gaussian priors, limiting both efficiency and effectiveness. To address these limitations, we propose GiFlow, a Graph-Informed Flow Matching framework for spatiotemporal imputation. GiFlow replaces the typical Gaussian prior with a graph-informed prior constructed via spatiotemporal filtering of observable signals, which better aligns the source distribution to the target and thereby simplifies the generation trajectory. The flow field is parameterized by a hybrid vector field model that integrates spatial attention, temporal attention, and spatiotemporal propagation, enabling joint modeling of spatial and temporal dependencies. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed GiFlow outperforms the state-of-the-art approaches in spatiotemporal imputation. The code is available at https://github.com/zepengzhang/GiFlow.

Unpaired RGB-Thermal Gaussian-Splatting Using Visual Geometric Transformers

Multi-modal novel view synthesis (NVS) combining RGB and thermal imagery enables precise 3D scene reconstruction with visual and thermal information. However, existing methods typically rely on precisely calibrated RGB-thermal image pairs or stereo setups, limiting scalability and practical deployment. To address this, we introduce a framework for unpaired RGB-thermal NVS that leverages VGGT, a 3D feed-forward transformer architecture, to independently estimate camera poses for each modality. The pose sets are then aligned using the Procrustes algorithm with a cross-modal feature matcher, enabling joint registration without paired calibration. Building on this alignment, we further propose a multi-modal 3D Gaussian Splatting approach that learns directly from unpaired RGB and thermal images. Experiments on diverse scenes demonstrate that our method achieves competitive performance in thermal view synthesis while maintaining RGB fidelity. Moreover, we show that existing reconstruction approaches can produce modality-specific reconstructions that lack cross-modal consistency. We thus introduce a benchmarking framework to rigorously evaluate both per-modality image synthesis and the multi-modal coherence of reconstructed scenes.

Towards Unified and Data-Efficient Prognostics and Health Management with Tabular Foundation Models

Data-driven Prognostics and Health Management (PHM) uses time-varying condition-monitoring data to diagnose system states and estimate remaining useful life in engineered assets. These tasks are central to maintenance planning, but industrial PHM data are often fragmented, partially observed, and poorly labeled, which hinders supervised learning. Foundation models offer a route toward reusable predictive systems, yet most time-series foundation models are designed for forecasting and assume long, coherent, regularly sampled sequences. To address this gap, we propose a framework for applying Tabular Foundation Models to industrial time series using in-context learning, and we evaluate them on a variety of PHM tasks. By converting raw unit-level signals into tabular rows, we show that these models perform well across multiple tasks - including prognostics, and diagnostics - and are highly data efficient. We compare them directly with sequence models, transformer baselines, and gradient-boosted trees under a common evaluation protocol. The results indicate that tabular foundation models achieve the best average ranks across prognostic and diagnostic tasks. Our findings further show that PFN-based models are competitive in low-data regimes, that temporal context can be preserved in the tabular representation, and that performance depends on representative context construction under subsampling. These results demonstrate that tabular foundation models provide a practical and general interface for heterogeneous PHM problems.