DeepTherm: Deep Learning for Thermal Science

• DeepTherm is a deep learning approach that integrates thermodynamic transport physics with data-driven modeling to rapidly simulate and forecast thermal phenomena.
• It employs architectures like CNNs, operator networks, and hybrid models to encode physics constraints, achieving high-fidelity accuracy and inference speed-ups of 10³–10⁵×.
• Validated in diverse applications—from groundwater and IC thermal simulation to medical diagnostics and heatwave prediction—DeepTherm offers real-time, robust, and generalizable solutions.

DeepTherm is a collective moniker for a class of deep learning–driven methods for modeling, forecasting, and imaging thermal phenomena in a range of applied domains, from geoscience and environmental control to medical diagnostics, materials characterization, and public health. Across these domains, DeepTherm architectures unify physics-driven modeling with modern neural networks, typically replacing computationally intensive numerical solvers or empirical heuristics with fast, accurate, and often more generalizable surrogates. Common to these approaches is the coupling of thermodynamic transport physics (diffusion, advection, radiation), problem-specific data, and advanced network architectures—including convolutional, operator-based, and ensemble models.

1. Physics-Grounded Deep Learning Architectures

DeepTherm methods encode thermal physics directly into the learning framework via data preprocessing, network design, or training objectives. In groundwater plume prediction, DeepTherm employs U-Net–style CNNs that receive precomputed 2D Darcy velocity fields $\mathbf{q}$ as input channels and output steady-state temperature perturbations, effectively learning the nonlinear mapping governed by coupled Darcy–advection–diffusion PDEs (Davis et al., 2023). For 3D-IC temperature simulation, operator-learning frameworks (e.g., DeepONet) directly map function-valued PDE boundary/source conditions to temperature field solutions, with physics-informed loss terms that enforce PDE and boundary residuals without explicit paired datasets (Liu et al., 2023). Other variants, such as the active-metamaterial controller, integrate experimental feedback from physical sensors (IR camera) and close the real-time loop with a neural net mapping N-point temperature profiles to actuator setpoints for active thermal management (Jin et al., 2023).

Table: Representative DeepTherm Architectures and Physical Bases

Domain	Architecture Type	Physics/Model Basis
Groundwater Plume	U-Net CNN	Darcy & advection–diffusion equations
3D-IC Thermal Simulation	DeepONet (Operator NN)	Poisson/Heat PDE with parametric BCs/sources
Adaptive Metamaterial	Fully Connected NN	Experimental thermal feedback, real-time control
Medical Infrared Imaging	Deep Semi-NMF + RF	Spatial pattern extraction via factorization
Public Health (Heatwaves)	Transformer + GLM	Sequence modeling of mortality and meteorology

2. Methodology: Data Generation, Representations, and Losses

DeepTherm approaches leverage both synthetic/physics-simulated and experimental data, with problem-specific preprocessing to align network inputs with the structure of the underlying physics.

• Data generation for CNN surrogates involves forward PDE solves (e.g., PFLOTRAN for groundwater cases, synthetic electromagnetic or thermal simulation for metamaterials) to build labeled pairs $(\mathbf{q}_{x,y}, \Delta T)$ over randomized heterogeneity and boundary conditions (Davis et al., 2023, Jin et al., 2023).
• Representation of physical fields adheres to natural discretizations; for subsurface models, all inputs/outputs are 2D grids, while for operator learning, input functions (e.g., boundary conditions, power maps) are sampled at "sensor" points and processed by dedicated branch networks (Liu et al., 2023).
• Loss functions incorporate both conventional error minimization (e.g., mean-squared error between predicted and reference fields or physical observables) and domain-specific constraints (physics-informed residual losses penalizing violation of governing PDEs and boundary conditions).

3. Domains of Application

DeepTherm frameworks have been validated across diverse domains, including:

• Subsurface Thermal Plume Modeling: Rapidly predicting downstream thermal impact of groundwater heat pumps including permeability heterogeneity and variable Darcy flows. The best-performing variants (TNG-Geo-Light) achieve RMSE ≈ 0.16 K relative to high-fidelity solvers, with over $10^3$–$10^4\times$ inference speed-up (Davis et al., 2023).
• Integrated Circuit (IC) Thermal Analysis: Operator learning–based surrogates (DeepOHeat) predict steady-state 3D temperature distributions of chips under arbitrary 2D/3D power and boundary conditions, generalizing instantly to new settings with mean absolute percentage errors down to $0.02\%$–$0.16\%$, and acceleration factors up to $10^5$ compared to commercial FEM tools (Liu et al., 2023).
• Active Thermal Metamaterials: Control systems combining infrared imaging, neural network mapping of environmental temperature distributions, and stepper-driven mechanical modulation to maintain or amplify internal gradients, validated with both simulation and experiment (Jin et al., 2023).
• Medical Infrared Diagnosis: Factorization-based DeepTherm variants for breast cancer screening combine deep semi-nonnegative matrix factorization, kernel-based feature selection, and ensemble classifiers to extract and classify spatial thermomic signatures, achieving 71.36% accuracy (CI 69.42%–73.30%) (Yousefi et al., 2021).
• Heatwave Early Warning: Sequence-to-sequence neural time series modeling of all-cause mortality in conjunction with classical baseline mortality regression enables early heatwave alarm signaling without explicit cause-of-death data, robust across years, regions, and demographics (Xu et al., 9 Dec 2025).

4. Performance Characteristics and Validation

DeepTherm models consistently demonstrate several key properties:

• High-fidelity accuracy: Across domains, errors converge to the range of 0.1–0.2 K RMSE (thermal fields) or less than 1% MAPE (function space surrogate models).
• Generalization: Operator-learning approaches (e.g., DeepOHeat) handle unseen input configurations (e.g., arbitrary power maps or heat transfer coefficients) without retraining, due to function-level learning.
• Speed: Across domains, once trained, DeepTherm models achieve inference times of 1–10 ms per sample (GPU), compared to seconds or minutes for conventional PDE solvers, enabling real-time or high-throughput applications.
• Stability: Architecture and training choices—such as physics-enforced loss, skip-connections, or hierarchical embedding—stabilize generalization in the presence of data or environmental perturbations.

Empirical validation protocols include large held-out test sets, cross-validation (e.g., LOOCV in medical domains), and full-replacement of traditional solvers within operational pipelines for weeks or longer, demonstrating robustness by real-time field use and extensive year-over-year, region-by-region analysis (Davis et al., 2023, Liu et al., 2023, Jin et al., 2023, Yousefi et al., 2021, Xu et al., 9 Dec 2025).

5. Limitations and Future Directions

Limits of current DeepTherm paradigms include:

• Physics regimes: Most frameworks are steady-state or rely on fixed system parameters (e.g., flow rates, background temperature, or geometry); extensions to fully transient, nonlinear, or multi-physics coupling remain under development (Davis et al., 2023, Liu et al., 2023).
• Data regimes: Model generality is constrained by the bounds of input parameterization and the representativeness of training data (e.g., permeability ranges, power map structure, or physical sensor coverage).
• Scalability and heterogeneity: Expansion to genuine 3D heterogeneity, time-dependent control, or non-rectilinear or meshless geometries may require integration with geometric deep learning (level sets, point clouds, GNNs) or hybrid multi-fidelity solvers.
• Operational deployment: Certain assumptions such as real-time, gap-free input data (city-level mortality, sensor noise, mechanical actuator reliability) must be addressed for field and scaling applications (Jin et al., 2023, Xu et al., 9 Dec 2025).

Proposed future enhancements span extension to time-dependent simulations, broadening of material and environmental heterogeneity, incorporation of uncertainty quantification, and modular integration with multi-physics systems. Integration with Fourier Neural Operator or Graph Neural Operator frameworks is anticipated for unstructured meshes and irregular geometries (Liu et al., 2023).

6. Significance and Impact Across Disciplines

DeepTherm methodologies define a new paradigm for physics-informed, data-driven modeling and control of complex thermal processes. By enabling orders-of-magnitude acceleration over legacy numerical solvers, while preserving core physical fidelity and expanding generalizability, DeepTherm supports decision-making and operational control in real-time engineering, environmental regulation, biomedical diagnostics, and risk management. In medical imaging and public health, DeepTherm approaches facilitate interpretable, data-efficient screening and early warning without bespoke hand-labeling, as in breast cancer thermomics and heatwave mortality prediction (Yousefi et al., 2021, Xu et al., 9 Dec 2025). In engineering, they enable fast, flexible throughput for design optimization, anomaly detection, and adaptive control, as in microchip thermal analysis and advanced metamaterials (Liu et al., 2023, Jin et al., 2023). The modularity of DeepTherm—encompassing operator learning, classical surrogates, and GPU-accelerated inference—positions it as a central framework for current and future interdisciplinary advances in computational thermodynamics.