Heat Diffusion

The fusion of hyperspectral (HS) and Light Detection and Ranging (LiDAR) data plays a crucial role in enhancing land-cover classification by jointly exploiting spectral, spatial, and structural cues. However, existing multimodal fusion methods still struggle to model long-range dependencies and complex anisotropic interactions while maintaining computational efficiency. This paper introduces M2Heat, a physics-inspired framework that investigates multimodal fusion through the lens of heat conduction. At its core, a physics-driven visual heat conduction module (vHeat) and enhanced Frequency Value Embeddings (FVEs) simulate anisotropic information flow, enabling the capture of global dependencies with sub-quadratic complexity and physical interpretability. This mechanism, combined with a hybrid spatial-frequency fusion strategy named Cross-Frequency Fusion (CFF) module, produces highly discriminative and robust feature representations. M2Heat achieves competitive overall performance on three benchmarks, i.e., Trento, Houston2013, and Augsburg, while providing an interpretable heat-conduction-guided perspective for multimodal feature fusion. These results indicate the potential of heat-conduction-guided neural operators for efficient and interpretable RS multimodal fusion. The source code is publicly available at https: /github.com/Weikan0425/M2Heat_HSI_LiDAR.

This paper addresses infinite-dimensional Bayesian inference for inverse problem of partial differential equations with model parameters in infinite-dimensional Hilbert space. To effectively incorporate prior information, we propose a novel continuous normalizing flows based infinite-dimensional model. Specifically, by introducing a well-defined neural ordinary differential equation in infinite-dimensional space, a simple reference measure can be transformed into a more complex measure which encodes the prior information. A corresponding theoretical framework is established to ensure the well-posedness of our proposed Bayesian prior in infinite-dimensional space. We also provide training methods of the prior for two distinct data settings, along with two sampling algorithms for the resulting Bayesian posterior. The proposed framework is applied to three representative inverse problems: the simple smooth inverse problem, inverse scattering problem, and the inverse heat conduction problem. Numerical experiments support the theoretical analysis and demonstrate the efficiency of the proposed algorithms.

Accurate modeling and forecasting of power transformer thermal behavior are critical for reliability, asset lifetime, and optimized power system operation. Numerical approaches such as finite element methods (FEM) and computational fluid dynamics (CFD) offer high fidelity but are computationally expensive, require complex mesh generation, and are often impractical for real-time or large-scale applications, particularly when transformer geometries are unknown. Lumped-parameter thermal models are more practical but depend on transformer-specific thermal constants and may fail to capture dynamic responses under varying operating and environmental conditions. Purely data-driven machine learning methods, including artificial neural networks, convolutional neural networks, and long short-term memory (LSTM) networks, have shown success in forecasting transformer temperatures but typically require large volumes of high-quality training data and may produce physically inconsistent or uninterpretable results. This paper develops a physics-aware Neural Ordinary Differential Equation (Neural ODE) framework for forecasting transformer thermal behavior from real-world time-series data. Neural ODEs model system dynamics in continuous time, providing smooth trajectory prediction and a natural representation of continuously evolving thermal dynamics. A key contribution is the integration of simplified heat-transfer equations directly into the Neural ODE formulation. The model is evaluated across datasets from fifteen transformers in different regions of Norway with varying designs and cooling mechanisms. The results demonstrate that the developed Neural ODE framework provides a standardized, physics-aware, and robust forecasting approach for heterogeneous transformer units.

Divertor heat-flux analysis is essential for understanding plasma-wall interactions and protecting plasma-facing components in magnetic-confinement fusion devices, while conventional infrared-based inversion is usually performed after discharge and requires heat-conduction modeling with device-specific material properties, divertor geometry, and boundary conditions. Rather than accelerating this conventional infrared-based inversion paradigm, we introduce a new online-oriented signal-based reconstruction paradigm that directly reconstructs time-resolved radial heat-flux profiles from multi-source macroscopic plasma-state signals available during discharge. To enable systematic study of this task, we construct \textbf{DivMPS2HF}, a multi-source discharge dataset that provides the data foundation and benchmark for signal-based divertor heat-flux reconstruction. We further propose \textbf{SafeDivertor}, a task-driven framework designed to address the key challenges of signal-based heat-flux reconstruction. It employs physical prior-aware initialization to provide radial-distribution guidance for target channels, input perturbation to reduce over-reliance on specific heterogeneous signals, spectral-aware reconstruction optimization to exploit time-frequency priors and preserve transient dynamics, and progressive training to stabilize the optimization of these complementary objectives. Experiments on DivMPS2HF demonstrate that SafeDivertor achieves the best overall performance among the evaluated time-series baselines across all five metrics, establishing a new performance benchmark for signal-based divertor heat-flux reconstruction. The source code will be released on https://github.com/Event-AHU/OpenFusion

Physics-informed neural networks (PINNs) combine sparse observations with physical equations, providing an important approach for modeling complex plasma processes and inferring unknown physical quantities. The steep-gradient pedestal of high-confinement-mode tokamaks is closely linked to plasma confinement and edge transport. Analyzing ion-temperature-gradient (ITG) drift waves in this region requires jointly identifying complex eigenfrequencies and reconstructing two-dimensional complex-valued mode fields. Localized high-frequency oscillations, strong real-imaginary coupling, and nonlinear coupling between the mode field and eigenfrequency challenge PINN representation and joint optimization. To address these challenges, we propose a physics-informed neural framework combining Fourier feature encoding, complex-valued feature propagation, and three-stage training. Under sparse observations and physical constraints, it jointly solves for the complex eigenfrequency and mode field of a representative ground-state ITG branch. Experiments show that the framework accurately recovers the target complex eigenfrequency and two-dimensional complex-valued mode field and outperforms representative PINN baselines. It also provides a basis for analyzing higher-order and multiple-branch drift-wave modes.

Identifying cost-effective indigenous building materials that minimise heat penetration through walls is critical for indoor thermal comfort in low-income rural housing in hot-dry climates, where summer temperatures routinely exceed 45 C. We present a two-stage computational framework for thermal ranking of five low-cost indigenous wall materials: mud brick, clay-straw adobe, lime-stabilised bamboo panel, fired clay brick, and lime-mud composite. First, a validated Crank-Nicolson finite difference method (FDM) solves the one-dimensional transient heat equation with Robin boundary conditions under diurnal solar and outdoor air-temperature forcing, generating 1500 periodic-day solutions across a nine-dimensional parameter space by Latin Hypercube sampling. Second, a Physics-Informed Neural Operator (PINO) with a Fourier Neural Operator (FNO) backbone learns the parameter-to-solution operator mu -> T(x,t), enforcing both data fidelity and PDE consistency. The trained PINO attains a relative L2 field error of 5.14e-4 and a 0.201 K mean absolute error on the peak inner surface temperature, preserving the FDM material ranking exactly; PINO trained on 150 FDM samples matches a data-only FNO trained on twice as many, so the physics loss is most valuable when data are scarce. The periodic-day formulation also yields the ISO 13786 time lag and decrement factor, reproduced to within 0.99 h and 0.010. At nominal hot-dry summer conditions, clay-straw adobe achieves the best cost-performance index among widely available materials. A climate sweep, confirmed by FDM spot checks, reveals a regime boundary: under sub-ambient outdoor conditions the ranking inverts to conductive fired clay brick, delineating heat-exclusion and heat-rejection regimes. The framework supports evidence-based material selection for post-flood reconstruction in hot-dry regions.

In this paper, a parametric physics-informed neural network for solving the heterogeneous soil thermal problem with borehole heat exchangers (BHEs) as singular sources is developed. There are three novel features in the present framework; namely, (i) the singularity is naturally removed by using analytical line source models; (ii) using the explicit formulation for gradient thermal conductivity enables physics-informed learning of the parametrization featuring the conductivity; (iii) the learned correction is utilized as an efficient universal corrector via superposition principles. We first introduce the decomposition of the temperature change and transform the approximation of the entire heterogeneous response to the correction compensating the difference between the practical solution and idealized homogeneous approximation. In such a way, the delta function singularity is excluded and the bulk heat transfer is captured for the sake of facilitating the effective training of the neural network. The original problem is then reformulated as a governing correction diffusion or advection-diffusion equation subject to a homogeneous initial condition. The linearly varying thermal conductivity is used to model the soil heterogeneity. We propose a physics-informed neural network to approximate a universal corrector with respect to a single borehole with unit heat extraction rate. As a result, the network is trained by minimizing the physics-informed and data-anchored loss function that is evaluated for sampled conductivity parameters on adaptively selected training points. In addition, we include the location indicator function regarding the source as a feature input of network and find that it helps the network to process the local information. We perform numerical tests to exhibit the effectiveness of the proposed method based on three different analytical models.

Deep generative models offer a promising paradigm for topology optimization, enabling rapid design exploration. However, these approaches lack intrinsic physics guidance, often leading to poor generalizability across unseen boundary conditions and the formation of floating material artifacts. To address these limitations, we propose Hierarchical Physics-Guided Diffusion (HPG-Diff), a novel diffusion framework that enforces physics consistency through two synergistic mechanisms. First, we introduce a hierarchical physics-guided strategy that aligns different precomputed physics features with the denoising process, guiding material distribution toward optimal load paths to enhance generalizability. Second, we propose a floating material suppression loss as a differentiable connectivity constraint inspired by thermal conduction to improve topological connectivity. By simulating a virtual heat propagation process from load positions, this mechanism explicitly penalizes floating material during training. Quantitative evaluations demonstrate that HPG-Diff achieves average compliance errors of 0.87% (in-distribution) and 5.29% (out-of-distribution), while reducing floating material ratios to 2.90% and 2.44%, respectively. Furthermore, case studies on a 3:1 rectangular domain, including cantilever and bridge benchmarks, provide preliminary evidence that lightweight LoRA fine-tuning with a small dataset can support the adaptation of HPG-Diff to rectangular non-square domains.

Predicting thermal volatility in high-performance EV powertrains is difficult as internal temperatures are rarely observable outside the lab, and models calibrated on lab drive cycles fail when deployed against real-world loads. We study this lab-to-track transfer problem using conformal prediction, offering distribution-free uncertainty bounds. We implement Ensemble Batch Prediction Intervals (EnbPI; Xu & Xie, 2021), a leave-one-out bootstrap-ensemble conformal method for autocorrelated time series, and calibrate it on real CALCE lithium-ion cycler data (A123 SP20 cells, FUDS profile). We evaluate it under a genuine, measured covariate shift: a second real CALCE test condition (US06 Highway Driving Schedule at 45°C). The unweighted EnbPI bound, achieving its nominal 95% coverage in-distribution (measured: 95.00%), degrades to 70.13% empirical coverage under this real shift. We introduce a weighted EnbPI procedure combining EnbPI's ensemble residuals with density-ratio weighting (Tibshirani et al., 2019), estimating the density ratio via a probabilistic domain classifier. This recovers coverage to 72.42%, a modest, honestly-reported improvement, not a complete fix. We additionally apply the calibrated model to real 2023 Formula 1 telemetry (Monza and Silverstone, driver VER) as an unsupervised out-of-distribution diagnostic. Because no internal thermal channel exists in public trackside telemetry, we report only unsupervised flag rates (65.6% at Monza, 58.0% at Silverstone, well above the 5% in-distribution base rate) and note inconsistent associations between flags and braking/DRS zones. We conclude that conformal domain adaptation is a promising but only partially solved tool for this problem, detailing exactly where it falls short.

Accurate modeling of the divertor temperature field is essential for preventing material melting and damage and for extending the service life of fusion devices. However, conventional numerical methods, such as the Finite Element Method (FEM), are computationally expensive and therefore unsuitable for real-time applications. Therefore, a fast and generalizable method is required for real-time reconstruction of the divertor temperature field and subsequent real-time control. To address the above issue, we propose a Physics-aware Neural Operator Transformer (PNOT) to characterize the spatiotemporal evolution of the divertor temperature field. It models boundary heat-flux relations as a structured graph and employs graph attention to explicitly capture spatial physical dependencies. Inspired by physics-aware attention, we further develop a physics-aware neural operator module to aggregate query points with similar physical conditions via slicing and model heat diffusion, while a gradient-constrained Sobolev regularization loss enforces consistency between function values and their derivatives. Experimental results show that these physical constraints improve prediction accuracy while preserving physical consistency. The source code of this paper will be released on https://github.com/Event-AHU/OpenFusion

A growing number of techniques leverage the spatial structures that underlie many real-world datasets. Despite these advances, the complementary task of estimating spatial structures and understanding their role within these techniques has often been overlooked. In neurophysiological data analysis specifically, numerous methods exist to estimate brain connectivity, but most are not explicitly model-based, dynamic, multivariate, or directed. To address these limitations, we previously introduced noise-driven heat modelling on graphs for neurophysiological connectivity estimation. In this study, we extend this framework by relaxing earlier noise assumptions and adding regularisation to improve robustness. We also develop a simulation procedure to characterise and evaluate our technique in a controlled setting. Finally, we demonstrate that the technique is able to capture meaningful spatial structure across two experiments, each using two real-world datasets. The explicit model formulation of our connectivity estimator has the potential to improve the interpretability of graph-based techniques across a wide range of applications. The code implementing our method is available at https://github.com/sgoerttler/Heat_Connectivity.

Wood materials exhibit complex, spatially varying thermal properties that challenge traditional architectural assumptions of material homogeneity. Although data-driven approaches can directly map wood RGB images to their corresponding thermal responses, they operate as uninterpretable black boxes that prioritize statistical correlation and may absorb experimental noise rather than thermodynamic plausibility. To address these limitations, we present physics-informed deep learning frameworks that integrate partial differential equations (PDEs) to predict pixel-level thermal responses of spatially heterogeneous wood materials using wood RGB images and testbed temperature maps. Specifically, we investigate two distinct approaches to enforcing a normalized 2D steady-state heat transfer equation derived from the general heat transfer equation: Physics-Informed Convolutional Neural Networks (PICNNs), which embed physics as a soft penalty term in the loss function, and Physics-Integrated Convolutional Neural Networks (PInteCNNs), which hard-code an analytical approximator-predictor-corrector solver directly into convolutional neural networks. To validate our proposed approaches, we collect three real-world multimodal datasets of Poplar, Grandis Cross-Cut (Grandis-CC), and Grandis Radial-Cut (Grandis-RC) wood samples. We further demonstrate that embedding physical inductive biases successfully balances predictive accuracy, physical interpretability, and intra-species diversity, outperforming data-driven approaches in handling complex wood material heterogeneity and enabling the extraction of interpretable physical parameters. Project: https://zekifayes.github.io/pim

Multi-zone HVAC control is a spatial decision problem in which indoor thermal evolution and control decisions depend not only on outdoor conditions and internal heat gains but also on zone layout, physical adjacency, and delayed thermal interactions across the building. Recent LLM-based HVAC controllers have shown that prompt-based control is feasible. However, these methods typically rely on task descriptions, observation values, short textual feedback, or unstructured retrieval, which limits their ability to reason about zone coupling, thermal response, and building dynamics. This paper presents a thermodynamics-aware LLM control framework for a five-zone EnergyPlus building simulation. The controller is grounded in a physics-informed spatial knowledge graph derived from Brick-style building semantics and linked with recent interaction history. At each control step, the model receives the current building state, graph-structured spatial context, and recent environment-controller history, enabling it to make decisions that reflect both building structure and short-term thermal evolution. We evaluate the framework against standard control baselines and several LLM-based alternatives. Results show that the proposed approach achieves the best overall energy-comfort trade-off and the lowest PMV violation while maintaining energy-efficient operation.

Neural operators such as the Fourier Neural Operator (FNO) have emerged as powerful surrogates for solving partial differential equations (PDEs), achieving speedups of several orders of magnitude over traditional numerical solvers. However, deploying these models in safety-critical engineering applications -- such as thermal management of electronic components and battery systems -- requires not only accurate point predictions but also rigorous uncertainty guarantees. Existing uncertainty quantification (UQ) methods for neural operators, including Monte Carlo Dropout and Deep Ensembles, provide only relative uncertainty estimates without formal coverage guarantees. In this work, we propose the first application of split conformal prediction to neural operator-based physics simulation, providing distribution-free prediction intervals with finite-sample coverage guarantees. We further introduce a normalized conformal prediction scheme that leverages MC Dropout uncertainty to produce adaptive-width intervals, yielding tighter intervals in regions of low uncertainty and wider intervals where the model is less certain. Full-scale experiments (33.7M parameters, 800 training samples, 5 ensemble members, NVIDIA V100) on steady-state heat conduction benchmarks demonstrate that our method achieves 89.1% empirical coverage at the target level of alpha=0.1, while producing spatially adaptive prediction intervals that reflect the underlying physical uncertainty structure. We also provide an uncertainty decomposition framework that separates epistemic uncertainty (68% of total) from aleatoric uncertainty (32% of total), offering actionable guidance for data collection and model improvement. Our method is implemented in an open-source platform with REST API endpoints and interactive 3D visualization.

High-dimensional transient heat diffusion under noisy boundary conditions exposes a fundamental limitation of classical numerical methods: accuracy degrades catastrophically where physical noise is unavoidable. This paper presents a Physics-Informed Neural Network (PINN) framework as a systematic solution to this problem across one, two, and three spatial dimensions, establishing clear operational regimes that redefine solver selection in noisy thermal systems. Under 20% boundary noise in 3D, PINN sustains approximately 91% accuracy while Finite Difference Method (FDM) collapses to 36%, a clear decisive advantage. This is further confirmed in a physical copper thermal system, where PINN reduces boundary reconstruction error by 3.3 times under realistic noise conditions. This noise resilience is accompanied by a dimensionality-driven efficiency crossover: PINN requires fewer spacetime nodes than FDM in 3D while achieving superior accuracy, exposing the true cost of classical discretization at scale. These findings reframe solver selection: the decisive axis is not accuracy alone, but noise exposure and dimensionality jointly. When noise and dimensionality are both high, the classical solver paradigm is insufficient; this work provides the foundation to justify PINN as the operational standard in such regimes.

Artificial-intelligence surrogates can support second-by-second thermal-hydraulic forecasting, but models selected and frozen offline may become condition-locked once deployed outside their pretraining envelope. This study develops a guarded continual-adaptation framework for experimental thermal-hydraulic loop data in which role-separated agents - Monitor, Diagnosis, Adaptation, Safety-Auditor, and Orchestrator - diagnose error signatures, prioritize candidate model families, and review promotions, while deterministic champion-challenger gates and background shadow learning retain final authority over model replacement. Seven surrogate families were screened by blocked three-fold cross-validation, and a temporal Fourier neural operator was selected as the initial champion for 60-s-history-to-10-s-trajectory forecasting on two held-out transients, with three seeds per adaptive mode. Static deployment gave a channel-averaged MAE of 7.06 and a 56.8% warning-exceedance ratio; rule-based adaptation reduced MAE to 6.54, whereas shadow refresh alone remained close to Static. The MA-Full mode, in which the role-separated multi-agent council reviews every evaluated stream step, achieved the lowest mean error, 5.72, and 35.8% exceedance, corresponding to a 19.0% improvement over Static. Paired bootstrap intervals against Static excluded zero, although intervals among adaptive modes overlapped and the six paired units limit broad statistical claims. Validated promotions from the neural operator to Transformer and graph neural network indicate that logged, gate-controlled adaptation can support auditable surrogate evolution while deterministic gates retain deployment authority.

Real-time thermal-hydraulic simulation is essential for digital twin (DT) technology that supports the safe and efficient operation of small modular reactors (SMRs). Computational fluid dynamics (CFD) provides high-fidelity flow analysis, but its computational cost prevents direct use in DT applications. AI-based surrogate modeling has been actively investigated to address this limitation, yet neural operator--based surrogates for CFD-level transient analysis of SMR-specific geometries have not been reported. This study presents an integrated framework that combines a reduced-order model (ROM) with neural operators, applied to the helical coil steam generator (HCSG) of the System-integrated Modular Advanced Reactor (SMART). Two ROM strategies tailored to each CFD data type were compared, an MLP-based autoencoder (AE) for unstructured mesh data and a convolutional autoencoder (CAE) for structured mesh data, and each was coupled with the deep operator network (DeepONet) to construct the latent DeepONet (L-DeepONet). The Fourier neural operator (FNO) was additionally adopted for comparison. A multi-scale technique was incorporated into both frameworks to mitigate spectral bias and improve the prediction of Kármán vortex streets developing inside the HCSG. The multi-scale L-DeepONet captured the instantaneous periodic vortex dynamics in both velocity and pressure fields, while the FNO and its multi-scale variant predicted the time-averaged mean flow and provided reliable pressure drop estimates. These complementary characteristics provide a practical model-selection guideline that links each architecture to specific DT objectives based on CFD data type and the required level of flow resolution.

Machine learning (ML) is increasingly used for data-driven modeling of buildings to enable downstream tasks such as fault detection and diagnosis, and energy-efficient control. While recent work improves generalization across building characteristics, weather, and occupancy, generalization also depends on sufficient exploration of the control-driven system state space. Existing real-world datasets and simulation environments predominantly reflect stationary operation under fixed control policies, resulting in limited excitation and reduced robustness to unseen operating conditions. This paper introduces BuilDyn, a package based on BuilDa that enables customizable excitation strategies for control-oriented data generation. BuilDyn further supports sampling from representative building distributions and provides a Python interface for easy integration into machine learning pipelines. We demonstrate the benefits of BuilDyn by comparing the performance of data-driven ML models trained on non-excited and excited data for one building. With BuilDyn, we hope to advance scalable control-oriented modeling and support future directions such as transfer learning and building-specific foundation models.

Two-phase boiling enables heat transfer rates an order of magnitude higher than single-phase cooling, but it remains difficult to model due to the strong coupling between phase change, turbulence, and transport, as well as extreme sensitivity to fluid properties and thermodynamic conditions. Existing learning-based surrogates are either condition- or fluid-specific, limiting generalization and requiring separate models. We present NUCLEUS, a mixture-of-experts model for pool boiling that replaces collections of specialized surrogates with a single architecture. NUCLEUS combines neighborhood attention, signed distance field reinitialization for interface consistency, and expert routing that exhibits emergent specialization across distinct boiling dynamics. Trained on high-fidelity simulations of pool boiling, NUCLEUS jointly models saturated and subcooled boiling across three fluid classes (dielectrics, refrigerants, and cryogens), resolving failure modes of prior models on extreme fluids. We show that expert routing exhibits coherent spatial structure and specialization without explicit supervision. Quantitatively, NUCLEUS matches or exceeds baselines while maintaining physical consistency across heterogeneous boiling configurations. We also show zero-shot and few-shot generalization capabilities on downstream tasks such as a new fluid (Opteon 2P50 developed for immersion cooling). These results demonstrate that mixture-of-experts models are a scalable pathway toward unified surrogate modeling of boiling dynamics and lay the groundwork for broader generalization across scientific ML.

Autonomous space systems operating in extreme thermal environments require accurate and efficient thermal modeling to support both pre-mission system design and onboard autonomy. For lunar rovers, large temperature gradients, radiative heat transfer, and variable surface conditions make reliable thermal prediction especially challenging. High-fidelity physics-based simulations provide accurate results but are computationally expensive, while simplified models and lookup-table approach often lack sufficient accuracy. Physics-informed machine learning (PIML) offers a promising alternative by combining data-driven models with embedded physical knowledge. This paper presents a PIML framework for thermal analysis of a simplified lunar rover with internal heat sources, where machine learning enables environment-adaptive coarse meshing. The proposed architecture integrates a transfer neural network (TNN) that adaptively determines 3D finite-difference nodalization based on thermal loads and initial conditions, enabling more accurate coarse-mesh calculations. A differentiable finite-difference thermal simulator is embedded within the framework to enforce physical consistency and support efficient training, while an upscaling layer reconstructs high-resolution temperature fields from the coarse-grid solution. The proposed PIML approach is evaluated against high-fidelity fine-mesh simulations, low-fidelity fixed coarse-mesh models, and a purely data-driven artificial neural network (ANN). Results show that the PIML framework improves prediction accuracy by 50% and 39% relative to the coarse-mesh physics model and ANN model, respectively, while maintaining physically consistent thermal distributions. Computationally, the framework is also 3x faster than high-fidelity simulations, demonstrating an effective balance between accuracy and efficiency for thermal modeling of lunar rover systems.

Motor thermal management is often overlooked in the context of electrically-actuated robots, particularly legged robots, but motor overheating is a key factor that limits long-duration locomotion especially under payload conditions. This paper integrates a whole-body thermal model of a quadruped robot into the reinforcement learning pipeline to update motor temperatures, and proposes a two-stage training framework for motor thermal management. In this framework, a nominal policy is first pre-trained as a locomotion baseline capable of traversing diverse terrains. A residual policy is then trained on top of the nominal policy to provide corrective actions based on the robot's thermal state, ensuring high performance under low-temperature conditions and preventing motor overheating under high-temperature conditions. Simulation results demonstrate that the proposed policy achieves an effective balance between motor thermal safety and locomotion performance. Real-world experiments on a Unitree A1 quadruped robot further validate the approach: under a 3 kg payload, the robot achieves stable locomotion across multiple terrains for over 13 minutes, while the nominal policy alone leads to motor overheating in about 5 minutes.

Data-driven modeling is becoming central to multiphase transport, electronics cooling, acoustic diagnostics, and thermal-fluid digital twins, but progress is limited by fragmented datasets and raw instrument files that are difficult to decode, reuse, or benchmark. This paper presents an open ecosystem of multimodal datasets and open-source software packages developed by the Nano Energy and Data-Driven Discovery (NED3) Laboratory for reproducible AI-enabled thermal-fluid research. We introduce a spatial-plus-temporal dimensionality framework, denoted S+TD, to classify datasets by the dimensionality of measured or simulated fields, including 0+0D point values, 0+1D time series, 1+0D profiles, 2+0D images, 2+1D videos, 3+0D volumetric fields, and multimodal combinations. We organize public NED3 datasets spanning boiling images, acoustic and thermal measurements, high-speed videos, infrared thermography, thermal-resistance measurements, CFD-generated fields, design files, and acoustic-emission data. We also describe complementary software packages, including BubbleID, SeqReg, CFDTwin, IRISApp, decode-wfs, AELab, and FlowLab, which support computer vision, sequence regression, surrogate modeling, infrared analysis, waveform decoding, acoustic-emission analysis, and multimodal diagnostics. Particular emphasis is placed on SeqReg, a general sequence-regression library for 0+1D, 1+1D, and 2+1D data, with applications such as nonintrusive heat-flux estimation. Finally, we discuss future community efforts to build interoperable thermal-fluid databanks and curated AI/ML tool libraries that connect datasets, metadata, decoders, baselines, benchmarks, and physically interpretable models.

Diffusion models are widely used in image generation, with most relying on noise-based corruption and denoising. A distinct branch instead uses blur as the main corruption, preserving better color budgets and multi-scale detail by providing multi-scale priors. However, blur-based models remain in SDE-based frameworks and are not integrated into ODE-based frameworks, such as Flow Matching (FM). Meanwhile, in the blur-based formulation, the classical inverse heat-dissipation (IHD) process faces an ill-posed challenge. Moreover, under the data-manifold assumption, regressing blurred images from high-dimensional noise (or velocity) space is also difficult. We propose Heat Dissipation Flow Matching (HDFM), which introduces a continuous blurred (heat-dissipation) process into FM to inject multi-scale priors. HDFM aligns an interpolated heat-dissipation path to address ill-posedness and adopts $x$-prediction to mitigate high-dimensional regression difficulty. Toy experiments and ablation studies show that HDFM consistently benefits from both blur and $x$-prediction. The performance of HDFM outperforms most baseline methods on all datasets.

Continental-scale knowledge of subsurface temperature is limited by the cost and sparsity of borehole measurements, but such information is essential for geothermal resource assessment and for understanding heat transport in the shallow crust. The thermal field reflects the interaction between lithology, crustal structure, radiogenic heat production, and advective fluid flow, sometimes producing sharp anomalies that are smoothed by conventional interpolation or difficult to capture with physical models. Here we introduce In-Context Earth, a transformer-based model that uses sparse local borehole observations as geological context to predict continuous temperature-at-depth fields with calibrated uncertainty. In the contiguous United States, the model achieves a mean absolute error of 4.7 °C, outperforming the physics-informed Stanford Thermal Model, a model based on AlphaEarth embeddings, the multimodal Transparent Earth model, and universal kriging, while resolving sharper thermal gradients in geothermal provinces. Its uncertainty estimates are well calibrated, with a Kolmogorov-Smirnov statistic of 2.5%. Without finetuning, the model adapts to Alberta, Australia, and the United Kingdom (UK) using only 20 local observations at inference time, maintaining high accuracy in geologically distinct test regions with a mean absolute error of 2.2 °C in Alberta, 6.2 °C in Australia, and 5.4 °C in the UK. Interpretability analyses show that the model learns internal representations of subsurface properties it never observes during training, including seismic velocities, geochemistry, and crustal structure, and uses these representations in physically consistent ways. More broadly, this work shows that in-context learning can use sparse borehole observations for continental-scale subsurface characterization, without requiring dense measurements or region-specific retraining.

Neural network surrogate models have emerged as a promising approach to model solution fields for a wide variety of boundary value problems encountered in physical modeling. Stochastic problems represent an area of particularly high interest because of the potential to significantly reduce the repeated evaluation of expensive forward models via traditional numerical solvers when conducting parametric analysis. However, many studies found in the literature primarily focus on the ability of neural network surrogate models to represent deterministic samples or mean field solutions and largely overlook surrogate model performance at the tails of the distribution. The present study examines in detail the ability of neural network surrogate models to capture the full distribution of solution fields over the entire probability space, while emphasis is placed at the tails of the distribution. Serving as a canonical problem is the heat conduction equation with a highly stochastic source term, inducing extremely large variation in the thermal solution field. Comparisons are made between a classic feed-forward fully connected network and a Deep Operator Network architecture, using both data-driven and physics-informed loss functions. Results show that the worst-case prediction errors are an order of magnitude larger than the mean field error, highlighting the importance of the outlier samples. The large errors associated with extreme samples result from the networks having to extrapolate beyond the bounds of the training data. A method for identifying these samples is presented along with a discussion of potential approaches to account of their errors. Among the models considered, the fully connected neural network trained using a weak form residual loss performs best in handling these extrapolated inputs, achieving the highest prediction accuracy for the numerically produced datasets.

Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend the conditional entropy of heat diffusion from static graphs to temporal networks and study its properties. We provide an upper bound and explain how discrepancies from it arise from the presence of asymmetric temporal paths. Moreover, we show that this quantity is monotone in time, yielding an information-theoretic analog of the second law of thermodynamics for inhomogeneous diffusion on temporal networks. We then introduce a local version of conditional entropy, designed to probe diffusion over finite temporal windows, and show that it provides an informative signal for change-point detection in continuous-time temporal networks. We evaluate the proposed methodology on synthetic benchmarks, including comparative experiments with existing nonparametric baselines in the snapshot setting, and then apply it to a real-world temporal contact network from a French primary school. Finally, we show how to use detected change points to perform community detection on targeted sub-intervals, improving the quality and interpretability of the clustering results.

Obtaining an accurate short-term forecasting for heat demand is an essential part of operating district heating networks cost-efficient and reliable. Heat consumption time series at the building level are highly dependent on exogenous variables such as outdoor temperature and individual usage patterns, making forecasting in this context a challenging task. Thus, this paper benchmarks novel Transformer-based and xLSTM architectures for short-term heat-demand forecasting. Using hourly data from 25 German buildings (2017-2025), we compare three-hour and 24-hour forecasting horizons relevant for intraday control and day-ahead scheduling. We establish a multi-building benchmark that tests whether models trained on pooled, heterogeneous building data are able to generalize across diverse building stock. The results show that the xLSTM achieves the lowest RMSE (19.88 kWh for three-hour, 21.47 kWh for 24-hour forecasts), while the Temporal Fusion Transformer attains the best MAE (9.16 kWh for three-hour forecasts). As xLSTMs and Transformers require long training times and have a huge number of trainable parameters, their sustainability remains questionable. Therefore, this paper further investigates the trade-off between predictive accuracy and computational resource demand of the evaluated forecasting models. The findings indicate that also low-parameter models like a traditional fully-connected network achieve good predictive results, highlighting that marginal accuracy gains of the novel prediction models come at substantial resource expense for this use case.

Real-time supervisory control of thermal energy distribution systems requires digital twins that are accurate, interpretable, and uncertainty-aware, yet remain data and computationally efficient. High-fidelity simulations alone are costly, while purely data-driven surrogates often lack robustness. To address these challenges, this work proposes an active learning (AL) framework that couples system-level Modelica simulations with four simpler physics-informed and data-driven surrogate modeling approaches: deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC), its probabilistic multivariate-Gaussian extension (MvG-SINDyC), feedforward neural network (FNN), and gated recurrent unit (GRU) network. Tailored to each surrogate, model-specific AL query strategies are employed, including Mahalanobis-distance sampling in coefficient space for MvG-SINDyC and error-based sampling in prediction space for SINDyC, FNN, and GRU, allowing the learning process to prioritize dynamically informative trajectories. The proposed approach is demonstrated on the glycol heat exchanger (GHX) subsystem of the Thermal Energy Distribution System (TEDS) at Idaho National Laboratory. Across key GHX outputs--the bypass mass flow rate $\dot{m}_{\mathrm{GHX}}$ and heat transfer rate $Q_{\mathrm{GHX}}$-the AL framework achieves comparable predictive accuracy using as few as one-fifth of the simulation trajectories required by random sampling. Among the evaluated surrogates, the GRU achieves the highest predictive fidelity, while SINDyC remains the most computationally efficient and interpretable. The probabilistic MvG-SINDyC surrogate further enables uncertainty quantification and exhibits the largest computational gains under AL.

The building energy community lacks a foundational thermal model, i.e., a single pretrained model capable of generalizing across diverse buildings, climates, and control strategies without building-specific calibration. Achieving this vision requires architectural principles that capture universal thermal dynamics rather than memorizing building-specific patterns. We take a step toward this goal by presenting a physics-informed transformer architecture that embeds domain knowledge, e.g., derivative enrichment and Euler-based numerical integration, into a decoder-only framework. We incorporate static building features extracted from simulation models and employ Rotary Position Embedding attention to capture temporal dependencies. Evaluated on the CityLearn dataset spanning 247 residential buildings across three climate zones, our model achieves one-step prediction accuracy (RMSE of 0.30°C in Texas, 0.29°C in Vermont) while outperforming both traditional baselines and fine-tuned Time-Series Foundation Models. We also demonstrate zero-shot transferability: models trained on as few as two buildings generalize to unseen buildings and climate zones without fine-tuning. Despite the limitation of simulated residential buildings, our results establish physics-informed architectural principles as a promising foundation for universal building thermal models.

In recent years, physics-informed neural networks (PINNs) have gained significant attention for solving differential equations, although they suffer from two fundamental limitations, namely, spectral bias inherent in neural networks and loss imbalance arising from multiscale phenomena. This paper proposes an adaptive wavelet-based PINN (AW-PINN) to address the extreme loss imbalance characteristic of problems with localized high-magnitude source terms. Such problems frequently arise in various physical applications, such as thermal processing, electro-magnetics, impact mechanics, and fluid dynamics involving localized forcing. The proposed framework dynamically adjusts the wavelet basis function based on residual and supervised loss. This adaptive nature makes AW-PINN handle problems with high-scale features effectively without being memory-intensive. Additionally, AW-PINN does not rely on automatic differentiation to obtain derivatives involved in the loss function, which accelerates the training process. The method operates in two stages, an initial short pre-training phase with fixed bases to select physically relevant wavelet families, followed by an adaptive refinement that adapts scales and translations without populating high-resolution bases across entire domains. Theoretically, we show that under certain assumptions, AW-PINN admits a Gaussian process limit and derive its associated NTK structure. We evaluate AW-PINN on several challenging PDEs featuring localized high-magnitude source terms with extreme loss imbalances having ratios up to $10^{10}:1$. Across these PDEs, including transient heat conduction, highly localized Poisson problems, oscillatory flow equations, and Maxwell equations with a point charge source, AW-PINN consistently outperforms existing methods in its class.

Accurate temperature estimation of pouch cells with indirect liquid cooling is essential for optimizing battery thermal management systems for transportation electrification. However, it is challenging due to the computational expense of finite element simulations and the limitations of data-driven models. This paper presents a physics-informed machine learning (PIML) framework for the efficient and reliable estimation of steady-state temperature profiles. The PIML approach integrates the governing heat transfer equations directly into the neural network's loss function, enabling high-fidelity predictions with significantly faster convergence than purely data-driven methods. The framework is evaluated on a dataset of varying cooling channel geometries. Results demonstrate that the PIML model converges more rapidly and achieves markedly higher accuracy, with a 49.1% reduction in mean squared error over the data-driven model. Validation against independent test cases further confirms its superior performance, particularly in regions away from the cooling channels. These findings underscore the potential of PIML for surrogate modeling and design optimization in battery systems.

Accurate thermal modeling in metal additive manufacturing (AM) is essential for understanding the process-structure-performance relationship. While prior studies have explored generalization across unseen process conditions, they often require extensive datasets, costly retraining, or pre-training. Generalization across different materials also remains relatively unexplored due to the challenges posed by distinct material-dependent thermal behaviors. This paper introduces a parametric physics-informed neural network (PINN) framework for zero-shot generalization across arbitrary materials without labeled data, retraining, or pre-training. The framework adopts a decoupled parametric PINN architecture that separately encodes material properties and spatiotemporal coordinates, fusing them through conditional modulation to better align with the multiplicative role of material parameters in the governing equation and boundary conditions. Physics-guided output scaling derived from Rosenthal's analytical solution and a hybrid optimization strategy are further incorporated to enhance physical consistency, training stability, and convergence. Experiments on bare plate laser powder bed fusion (LPBF) across diverse metal alloys, including both in-distribution and out-of-distribution cases, demonstrate effective zero-shot generalizability along with superior training efficiency. Specifically, the proposed framework achieved up to a 64.2% reduction in relative L2 error compared to the non-parametric baseline while surpassing its performance within only 4.4% of the baseline training epochs. Ablation studies confirm that the proposed framework's components are broadly applicable to other PINN-based approaches. Overall, the proposed framework provides an efficient and scalable material-agnostic solution for zero-shot thermal modeling, contributing to more flexible and practical deployment in metal AM.

With the advent of system-in-package (SiP) chiplet-based design and heterogeneous 2.5D/3D integration, thermal-induced warpage has become a critical reliability concern. While conventional numerical approaches can deliver highly accurate results, they often incur prohibitively high computational costs, limiting their scalability for complex chiplet-package systems. In this paper, we present WarPGNN, an efficient and accurate parametric thermal warpage analysis framework powered by Graph Neural Networks (GNNs). By operating directly on graphs constructed from the floorplans, WarPGNN enables fast warpage-aware floorplan exploration and exhibits strong transferability across diverse package configurations. Our method first encodes multi-die floorplans into reduced Transitive Closure Graphs (rTCGs), then a Graph Convolution Network (GCN)-based encoder extracts hierarchical structural features, followed by a U-Net inspired decoder that reconstructs warpage maps from graph feature embeddings. Furthermore, to address the long-tailed pattern of warpage data distribution, we developed a physics-informed loss and revised a message-passing encoder based on Graph Isomorphic Network (GIN) that further enhance learning performance for extreme cases and expressiveness of graph embeddings. Numerical results show that WarPGNN achieves more than 205.91x speedup compared with the 2-D efficient FEM-based method and over 119766.64x acceleration with 3-D FEM method COMSOL, respectively, while maintaining comparable accuracy at only 1.26% full-scale normalized RMSE and 2.21% warpage value error. Compared with recent DeepONet-based model, our method achieved comparable prediction accuracy and inference speedup with 3.4x lower training time. In addition, WarPGNN demonstrates remarkable transferability on unseen datasets with up to 3.69% normalized RMSE and similar runtime.

Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ) capabilities. Most existing PINN-based prognostics approaches are deterministic or account only for epistemic uncertainty, limiting their suitability for risk-aware decision-making. This work introduces a heteroscedastic Bayesian Physics-Informed Neural Network (B-PINN) framework that jointly models epistemic and aleatoric uncertainty, yielding full predictive posteriors for spatiotemporal insulation material ageing estimation. The approach integrates Bayesian Neural Networks (BNNs) with physics-based residual enforcement and prior distributions, enabling probabilistic inference within a physics-informed learning architecture. The framework is evaluated on transformer insulation ageing application, validated with a finite-element thermal model and field measurements from a solar power plant, and benchmarked against deterministic PINNs, dropout-based PINNs (d-PINNs), and alternative B-PINN variants. Results show that the proposed B-PINN provides improved predictive accuracy and better-calibrated uncertainty estimates than competing approaches. A systematic sensitivity study further analyzes the impact of boundary-condition, initial-condition, and residual sampling strategies on accuracy, calibration, and generalization, and the influence of measurement noise on aleatoric uncertainty. Overall, the findings highlight the capability of Bayesian physics-informed learning to support uncertainty-aware prognostics and informed decision-making in transformer asset management by tracking aleatoric and epistemic sources of uncertainty.

The recent Segment Anything Model (SAM) demonstrates strong instance segmentation performance across various downstream tasks. However, SAM is trained solely on RGB data, limiting its direct applicability to RGB-thermal (RGB-T) semantic segmentation. Given that RGB-T provides a robust solution for scene understanding in adverse weather and lighting conditions, such as low light and overexposure, we propose a novel framework, SARTM, which customizes the powerful SAM for RGB-T semantic segmentation. Our key idea is to unleash the potential of SAM while introduce semantic understanding modules for RGB-T data pairs. Specifically, our framework first involves fine-tuning the original SAM by adding extra LoRA layers, aiming at preserving SAM's strong generalization and segmentation capabilities for downstream tasks. Secondly, we introduce language information as guidance for training our SARTM. To address cross-modal inconsistencies, we introduce a Cross-Modal Knowledge Distillation(CMKD) module that effectively achieves modality adaptation while maintaining its generalization capabilities. This semantic module enables the minimization of modality gaps and alleviates semantic ambiguity, facilitating the combination of any modality under any visual conditions. Furthermore, we enhance the segmentation performance by adjusting the segmentation head of SAM and incorporating an auxiliary semantic segmentation head, which integrates multi-scale features for effective fusion. Extensive experiments are conducted across three multi-modal RGBT semantic segmentation benchmarks: MFNET, PST900, and FMB. Both quantitative and qualitative results consistently demonstrate that the proposed SARTM significantly outperforms state-of-the-art approaches across a variety of conditions. Code and pre-trained weights can be found at https://github.com/wahaha-debug/SARTM.

Transfer Learning (TL) is an emerging field in modeling building thermal dynamics. This method reduces the data required for a data-driven model of a target building by leveraging knowledge from a source building. Consequently, it enables the creation of data-efficient models that can be used for advanced control and fault detection & diagnosis. A major limitation of the TL approach is its inconsistent performance across different sources. Although accurate source-building selection for a target is crucial, it remains a persistent challenge. We present GenTL, a general transfer learning model for single-family houses in Central Europe. GenTL can be efficiently fine-tuned to a large variety of target buildings. It is pretrained on a Long Short-Term Memory (LSTM) network with data from 450 different buildings. The general transfer learning model eliminates the need for source-building selection by serving as a universal source for fine-tuning. Comparative analysis with conventional single-source to single-target TL demonstrates the efficacy and reliability of the general pretraining approach. Testing GenTL on 144 target buildings for fine-tuning reveals an average prediction error (RMSE) reduction of 42.1 % compared to fine-tuning single-source models.