Cova-PINN: Cross-Domain Conservation Physics-Informed Neural Network for Fluid-Solid Conjugate Heat Transfer in Complex Geometries

arXiv:2610.11108 · cs.LG, physics.flu-dyn · Submitted 2026-10-08 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: I'm Tom, and with me are Jane, Lu, senior AI researcher at Tsinghua, Meng, lead engineer at a mysterious AI startup and Lalam, the in-house Large Language Model.

Jane: Today's paper: "Cova-PINN: Cross-Domain Conservation Physics-Informed Neural Network for Fluid-Solid Conjugate Heat Transfer in Complex Geometries".

Tom: The gist The Cova-PINN framework introduces a multi-domain PINN approach that aligns conservation support with thermal interaction paths to solve fluid–solid conjugate heat transfer (CHT) in complex geometries,

Jane: First, who's behind it and why it matters.

Paper summary: Tom: So we're building on what we just talked about. We're looking at how this paper, Cova-PINN: Cross-Domain Conservation Physics-Informed Neural Network for Fluid-Solid Conjugate Heat Transfer in Complex Geometries, tackles the core issue of multi-domain PINNs in heat transfer.

Jane: The central thesis is that standard methods enforce equations on separately sampled domain supports which can yield plausible temperature fields but result in inaccurate end-to-end energy transfer and outlet temperatures.

Lu: Cova-PINN proposes a multi-domain PINN framework that aligns conservation support with the thermal interaction paths in complex geometries. It claims this approach jointly optimizes cross-domain composite control-volume balances at the local scale and paired-wall closure at the global exchanger scale.

Meng: So, it’s moving beyond just solving physics in separate pieces; it’s about linking those pieces together based on how heat actually flows between them.

Tom: Right. The paper is evaluating this framework on four triply periodic minimal surface heat exchangers and a DualMS design against CHT specific, optimization-oriented, and complex geometry PINN baselines under a common protocol.

Jane: The key takeaway is that by aligning conservation support with the thermal interaction path in these complex geometries, they get better results than just training the flow networks separately.

Lu: They show that this alignment leads to reductions in average outlet temperature and device-level closure errors compared to MUSA-PINN-CHT.

Meng: It sounds like the paper is showing a systematic way to improve the energy balance calculation, not just a nice visualization of temperature.

Conclusion: Tom: Looking at the work by Zhang, Xie, Pan, and Lu on Cova-PINN: Cross-Domain Conservation Physics-Informed Neural Network for Fluid-Solid Conjugate Heat Transfer in Complex Geometries, this paper is really about making PINNs more useful for complex physical systems like heat exchangers.

Jane: Simply put, it means that when you use these neural networks to model things with different materials and fluids interacting, you need a strategy to make sure the energy isn't just balanced locally but also across the entire system.

Lu: It suggests that coupling local conservation objectives with global paired-wall closure is a good way to ensure that your simulation actually reflects how heat moves through the whole device, not just pieces of it.

Meng: For someone who only listens to this show, it means that if you're doing complex simulations where different physical domains meet, you need to think about linking those connections explicitly in the model's training setup.

Tom: Yeah. It points toward a future where we can use these PINNs for more reliable and accurate predictive modeling of real-world heat transfer equipment with intricate designs.

Jane: It’s about making sure the AI isn't just guessing plausible fields, but that it’s actually respecting the physical laws governing the total energy flow through the system.

Weizheng Zhang, Xunjie Xie, Hao Pan, Lin Lu

Shandong University · Tsinghua University

cs.LG, physics.flu-dyn

Submitted: 2026-10-08

Updated: 2026-10-08

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 90/100

The gist: The gist The Cova-PINN framework introduces a multi-domain PINN approach that aligns conservation support with thermal interaction paths to solve fluid–solid conjugate heat transfer (CHT) in

Key concepts

Cross-Domain Conservation Gap
This occurs when separately trained parts of a model, like fluid and solid domains, fail to correctly balance energy conservation across their shared interface. Cova-PINN tackles this by ensuring local conservation objectives connect the physics between the different materials along the thermal interaction path.
Local Cross-Domain Composite Control Volumes
These are specially designed regions constructed around heat transfer walls and extending into adjacent material areas. They enforce a compact energy balance by aggregating flux contributions from all intersected media, ensuring that energy is conserved locally across the fluid-solid boundaries.
Global Paired-Wall Heat-Rate Closure
This module provides a device-scale constraint by pairing the hot fluid–solid interface with the solid–cold fluid interface. It evaluates heat rates from both sides of the solid, which helps update only the solid temperature network to ensure overall energy balance across the entire exchanger.
Annealed Solid-Mean Temperature Regularization
This is a zero-order regularization technique used early in training. It anchors the average temperature of the solid domain against an expected inlet heat capacity rate, preventing initial implausible temperature drifts and decaying its influence as training progresses.

Terminology

Summary

The gist The Cova-PINN framework introduces a multi-domain PINN approach that aligns conservation support with thermal interaction paths to solve fluid–solid conjugate heat transfer (CHT) in complex geometries, significantly reducing end-to-end energy transfer and outlet temperature errors compared to existing baselines.

How it works

Cova-PINN addresses the cross-domain conservation gap where separately trained domain supports fail to close the device-scale energy balance, which is crucial in CHT problems. The framework employs a two-stage procedure: Stage 1 involves independently training and freezing the two MUSA-PINN flow networks, and Stage 2 jointly optimizes the thermal parameters by coupling local conservation objectives with global paired-wall closure.

The optimization objective is structured around three complementary components:

  1. Local Cross-Domain Composite Control Volumes: These volumes are constructed around the heat-transfer walls and extend into adjoining material regions along the thermal interaction path, and they enforce a compact balance of energy fluxes across all intersected media. The local loss is defined by Equation (8), which aggregates flux contributions from all material regions intersected by its support, connecting the hot-fluid–solid–cold-fluid interaction path.

  2. Global Paired-Wall Heat-Rate Closure: This module provides the complementary device-scale constraint by pairing the hot fluid–solid interface and the solid–cold fluid interface to evaluate both heat rates from the solid, leading to a residual loss that updates only the solid temperature network.

  3. Annealed Solid-Mean Temperature Regularization: To prevent early drift toward implausible levels during initial training, this zero-order regularizer anchors the solid-domain mean temperature against an average inlet heat capacity rate, and its weight decays linearly to zero over the first half of training.

Key Contributions and Performance

The paper demonstrates that domain-wise pointwise training can yield inaccurate exchanger-level energy transfer even when it reconstructs plausible temperature fields. Cova-PINN's support-aligned global–local conservation co-optimization framework is introduced, which couples finite-region transfer through wall-centered composite control volumes and paired-wall closure across the exchanger scale.

The framework was evaluated on four triply periodic minimal surface (TPMS) heat exchangers and a geometrically distinct DualMS design against CHT-specific, optimization-oriented, and complex-geometry PINN baselines. Relative to the closest baseline, MUSA-PINN-CHT, Cova-PINN reduces average outlet-temperature and device-level closure errors across the four TPMS topologies by 37.7% and 60.2%, respectively.

Comparative Results

The performance gains are substantial across various metrics:

** Efield**

Cova-PINN reduces average Efield by 28.6% relative to MUSA-PINNCHT across four TPMS topologies. On the more complex DualMS exchanger, Cova-PINN reduces Efield by 19.9%.

** Eout**

Cova-PINN achieves a 68.1% reduction in outlet error on the DualMS exchanger compared to MUSA-PINN-CHT.

** EQ**

The independently evaluated EQ also falls by 44.8%, confirming more accurate exchanged heat rather than closure alone.

Ablation Studies

Controlled leave-one-component-out studies confirm the complementary roles of the three objectives: removing Global Closure (G) gives the largest field error, while removing Solid-Mean Regularization (R) most strongly harms outlet and closure accuracy. This confirms that conservation support alignment is an effective principle for multi-domain physics learning.

Future work will extend support-aligned conservation to coupled and transient thermofluid problems, learn adaptive control-volume placement from geometry and residuals, and develop sparse quadrature. The present study establishes conservation-support alignment as an effective principle for multi-domain physics learning.

The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning. The Cova-PINN framework successfully coordinates finite-region transfer through wall-centered composite control volumes and exchanger-scale transfer through paired-wall closure, while annealed solid-mean regularization conditions early training. The results establish conservation support alignment as an effective principle for multi-domain physics learning.

Improvements for AI systems

  1. Improved AI system can accurately predict device-level energy transfer by implementing support-aligned global–local conservation co-optimization, which jointly optimizes cross-domain composite control-volume balances at the local scale and paired-wall closure at the global exchanger scale.

  2. The system will exhibit a reduction in critical performance metrics, such as average outlet-temperature and device-level closure errors by up to 60.2% on triply periodic minimal surface (TPMS) heat exchangers when compared to baselines like MUSA-PINN-CHT.

  3. The system can maintain higher accuracy in predicting the total energy transfer fidelity, as demonstrated by reducing the device-level energy imbalance error, Eclo, by 60.2% across TPMS topologies and 71.6% on DualMS exchangers compared to MUSA-PINN-CHT.

  4. The system will be more robust against training pathologies in complex geometries because it introduces an early optimization phase using the annealed solid-mean regularization term, which conditions early optimization and then decays to zero.

  5. The system can achieve superior field reconstruction accuracy by leveraging a multi-scale approach where the local module evaluates a compact balance defined by cross-domain control volumes that couple finite-region transfer, paired-wall closure coordinates exchanger-scale transfer.

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