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  "path": "/t/choosing-a-surrogate-model-architecture-to-predict-steady-state-thermal-fields-from-cad-geometry-fno-vs-pinn-vs-gnn/176615#post_2",
  "publishedAt": "2026-06-09T00:19:24.000Z",
  "site": "https://discuss.huggingface.co",
  "tags": [
    "Hugging Science Discord",
    "MeshGraphNets paper",
    "MeshGraphNets project page",
    "X-MeshGraphNet",
    "PhysicsNeMo MeshGraphNet tutorial",
    "Geo-FNO JMLR",
    "Geo-FNO arXiv",
    "GINO arXiv",
    "GINO OpenReview",
    "PhysicsNeMo DoMINO example",
    "PhysicsNeMo",
    "DeepOHeat",
    "DeepOHeat GitHub",
    "DeepOHeat-v1",
    "PINO",
    "PINN stiff-PDE instability discussion",
    "BRepNet",
    "BRepNet GitHub",
    "SIMSHIFT",
    "REALM",
    "MeshGraphNets: Learning Mesh-Based Simulation with Graph Networks",
    "X-MeshGraphNet: Scalable Multi-Scale Graph Neural Networks for Physics Simulation",
    "PhysicsNeMo GitHub",
    "Geo-FNO",
    "GINO",
    "DoMINO / PhysicsNeMo",
    "NVIDIA PhysicsNeMo GitHub",
    "Geo-FNO: Fourier Neural Operator with Learned Deformations for PDEs on General Geometries",
    "GINO: Geometry-Informed Neural Operator for Large-Scale 3D PDEs",
    "DoMINO / PhysicsNeMo external aerodynamics example",
    "DeepOHeat: Operator Learning-based Ultra-fast Thermal Simulation in 3D-IC Design",
    "DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design",
    "PINO: Physics-Informed Neural Operator for Learning Partial Differential Equations",
    "BRepNet: A topological message passing system for solid models",
    "SIMSHIFT: A Benchmark for Adapting Neural Surrogates to Distribution Shifts",
    "REALM benchmark"
  ],
  "textContent": "This is specialized enough that I’d strongly recommend asking in the Hugging Science Discord as well. I’m not a thermal/CAE practitioner myself, so please treat the notes below as a public-literature map rather than field-tested engineering advice.\n\n* * *\n\n## Short answer\n\nI would not frame this mainly as **vanilla FNO vs vanilla PINN vs vanilla GNN**.\n\nFor CAD/thermal surrogates, the first decision is usually the **representation** :\n\n  * CAD B-rep?\n  * surface mesh?\n  * volume FEM/CFD mesh?\n  * STL / point cloud?\n  * SDF / voxel grid?\n  * structured chip/package power map?\n\n\n\nGiven your description — _steady-state temperature fields from parameterized geometry plus boundary conditions, with expensive CFD/thermal solves and concern about hotspots / extrapolation_ — my practical starting point would be:\n\n  1. **If you already have FEM/CFD meshes:** start with a **mesh-GNN / MeshGraphNet / X-MeshGraphNet / graph neural operator** baseline.\n  2. **If you want FNO-like operator learning on irregular CAD geometries:** look at **Geo-FNO** , **GINO** , and related geometry-aware neural operators.\n  3. **If the problem is closer to 3D-IC / chip/package / power-map thermal analysis:** look at **DeepOHeat / DeepONet / FNO-style thermal operator learning**.\n  4. **I would not use a vanilla PINN as the primary engineering surrogate by default.** I would use PINN/PINO-style physics residuals, weak-form losses, calibration, or solver refinement as auxiliary pieces.\n\n\n\nA simple first recommendation:\n\n> **Build a strong mesh-GNN or graph neural operator baseline first, compare it against a geometry-aware neural operator such as GINO/Geo-FNO/DoMINO, and treat PINN-style physics as a regularizer or refinement stage rather than the main model.**\n\n## Why this is not just “FNO vs PINN vs GNN”\n\nThe architecture choice depends heavily on how geometry enters the model.\n\nInput representation | Natural model family | Why it matters\n---|---|---\n**Volume FEM/CFD mesh** | MeshGraphNet, X-MeshGraphNet, graph neural operator | Preserves unstructured simulation topology directly.\n**Surface mesh / STL / point cloud** | X-MeshGraphNet, DoMINO, GINO, point-cloud operator models | Useful if you want to avoid full meshing at inference time.\n**Irregular domain but FNO-like operator desired** | Geo-FNO, GINO | Standard FNO is tied to regular grids; geometry-aware variants try to recover FNO efficiency on irregular geometry.\n**Voxel / SDF grid** | 3D CNN, U-Net, FNO, ViT-style surrogates | Can work well if resolution and memory are manageable.\n**3D-IC / chip/package power maps** | DeepOHeat, DeepONet, FNO variants | The inputs are often more structured: layers, power maps, boundary conditions, materials.\n**Native CAD B-rep** | BRepNet / UV-Net-style geometry encoder + downstream surrogate | CAD geometry may be better represented before converting to mesh/point cloud, depending on workflow.\n\nSo I would start with:\n\n> **representation → data strategy → architecture → validation metrics**\n\nrather than architecture alone.\n\n## Architecture map\n\nModel family | When I would try it | Strengths | Main cautions | Useful links\n---|---|---|---|---\n**MeshGraphNet / mesh GNN** | You already have unstructured FEM/CFD meshes. | Natural fit for mesh-based simulation data; handles irregular topology better than regular-grid CNN/FNO baselines. | Vanilla message passing can struggle with long-range diffusion, very large 3D meshes, and mesh-resolution shift. | MeshGraphNets paper, MeshGraphNets project page\n**X-MeshGraphNet / scalable graph models** | Large 3D geometry, STL/point-cloud workflows, or when inference-time meshing is expensive. | Addresses scalability, partitioning, long-range interactions, and graph construction from tessellated geometry. | Still needs careful validation on thermal quantities, not just generic CFD metrics. | X-MeshGraphNet, PhysicsNeMo MeshGraphNet tutorial\n**Geo-FNO** | You like the FNO idea but your domain is not a simple rectangular grid. | Deforms irregular physical domains into a latent uniform grid where FFT/FNO can be applied. Accepts point clouds, meshes, and design parameters. | More complex than vanilla FNO; implementation/data pipeline may be less straightforward. | Geo-FNO JMLR, Geo-FNO arXiv\n**GINO** | Large 3D PDEs with varying geometries, SDF/point-cloud inputs, irregular grids. | Combines graph neural operators with Fourier neural operators; useful bridge between irregular geometry and FNO-like efficiency. | Mostly demonstrated on CFD/aerodynamics-style settings; thermal validation still needs task-specific checking. | GINO arXiv, GINO OpenReview\n**DoMINO / point-cloud CAE models** | CAD/STL/point-cloud industrial simulation surrogate workflows. | Designed around local, multi-scale point-cloud geometry modeling for industrial CAE-style tasks. | Public examples are often CFD/aero-heavy rather than exactly electronics thermal. | PhysicsNeMo DoMINO example, PhysicsNeMo\n**DeepOHeat / DeepONet thermal operators** | 3D-IC, chip/package, structured thermal maps, power maps, heat-transfer coefficients. | Very relevant if your geometry is closer to layered electronics / power-map thermal analysis than arbitrary mechanical CAD. | Less obviously suited to arbitrary CAD unless your representation can be made structured. | DeepOHeat, DeepOHeat GitHub, DeepOHeat-v1\n**PINO / physics-informed neural operator** | You have some data but want PDE constraints, higher-resolution residuals, or physics regularization. | Better framing than pure PINN for learning families of PDE solutions. | Still requires careful residual weighting, boundary-condition handling, and validation. | PINO\n**Vanilla PINN** | Inverse problems, sparse sensor reconstruction, parameter identification, or small single-instance problems. | Can encode governing equations directly. | Usually not my first choice for broad CAD-to-field surrogate learning across many geometries. Training stability and loss balancing can be painful. | PINN stiff-PDE instability discussion\n**B-rep geometry encoders** | Your real input is native CAD, not meshes. | Avoids losing CAD topology by prematurely converting to point clouds or meshes. | Usually only one piece of the pipeline; you still need a thermal field predictor downstream. | BRepNet, BRepNet GitHub\n\n## My practical baseline suggestion\n\nIf I had to design a first study, I would probably do this:\n\n### Phase 1 — Make the data split honest\n\nBefore comparing architectures, define validation splits that mimic the failure modes you actually care about.\n\nDo not rely only on random train/test splits.\n\nUse something like:\n\nSplit type | What it tests\n---|---\n**Random split** | Basic interpolation sanity check. Useful, but not enough.\n**Geometry-family holdout** | Can the model generalize to unseen shape families?\n**Boundary-condition holdout** | Does it extrapolate to new convection coefficients, inlet/outlet conditions, ambient temperatures, etc.?\n**Material-property holdout** | Does it handle new conductivity / heat capacity / anisotropy regimes?\n**Heat-source-layout holdout** | Does it generalize to new source positions, densities, or power maps?\n**Mesh-resolution shift** | Does it depend too much on the training mesh resolution?\n**Design-ranking split** | Does the surrogate preserve the ranking of candidate designs?\n\nFor this point, SIMSHIFT is especially relevant because it is explicitly about distribution shifts in industrial neural surrogates and includes a **heatsink design** task. I would also keep REALM in mind as a warning that simplified surrogate benchmarks can overstate real-world robustness.\n\n### Phase 2 — Build a mesh-based baseline\n\nIf you already have simulation meshes, I would start with a mesh-GNN baseline:\n\n  * node features: coordinates, material properties, source terms, boundary-condition flags, maybe distance-to-boundary / SDF-like features\n  * edge features: relative displacement, distance, possibly face/element connectivity features\n  * outputs: temperature field, maybe heat flux or derived quantities\n  * model: MeshGraphNet or an X-MeshGraphNet-style multi-scale variant\n\n\n\nWhy this first?\n\nBecause your problem sounds closer to **field prediction over an unstructured computational domain** than to image-to-image prediction.\n\nUseful starting points:\n\n  * MeshGraphNets: Learning Mesh-Based Simulation with Graph Networks\n  * X-MeshGraphNet: Scalable Multi-Scale Graph Neural Networks for Physics Simulation\n  * PhysicsNeMo MeshGraphNet tutorial\n  * PhysicsNeMo GitHub\n\n\n\n### Phase 3 — Compare against geometry-aware neural operators\n\nI would not compare against only vanilla FNO. I would compare against geometry-aware operator models:\n\n  * Geo-FNO\n  * GINO\n  * DoMINO / PhysicsNeMo\n  * possibly DeepONet-style variants if your input can be represented as functions over coordinates\n\n\n\nThe key point:\n\n> Vanilla FNO is attractive because it captures global structure efficiently, but its usual FFT formulation is most natural on regular grids. For irregular CAD geometry, use a geometry-aware variant or a hybrid graph/Fourier operator.\n\nGeo-FNO is a direct response to the regular-grid limitation: it learns a deformation from the irregular physical domain into a latent uniform grid. GINO is another useful framing: use graph neural operators to move between irregular grids and regular latent grids, where FNO-like layers can operate efficiently.\n\n### Phase 4 — Treat PINN-style physics as auxiliary\n\nI would not make a vanilla PINN the main baseline for this problem unless there is a specific reason.\n\nFor many design variants, repeatedly training or optimizing a PINN per geometry can become expensive and fragile. Hotspots, sharp gradients, stiff-like behavior, boundary loss balancing, and irregular geometry can make training difficult.\n\nBut physics-informed components are still useful:\n\nUse of physics | Practical form\n---|---\nRegularization | PDE residual loss, boundary-condition loss, flux consistency\nHigher-resolution correction | PINO-style loss at a finer resolution than training data\nTrust check | energy/flux residual as a diagnostic\nPost-processing | solver refinement or projection step\nActive learning | use residual or uncertainty to choose the next expensive simulation\n\nPINO is a better conceptual fit than a pure PINN if the goal is to learn a **solution operator** across a family of geometries / BCs / source terms.\n\n### Phase 5 — If the domain is 3D-IC / package thermal, check DeepOHeat\n\nIf your “electronics” problem is closer to chip/package thermal analysis than arbitrary CAD bodies, I would look carefully at the DeepOHeat line of work.\n\n  * DeepOHeat learns mappings from configurations such as boundary conditions, power maps, and heat-transfer coefficients to temperature fields in 3D-IC design.\n  * DeepOHeat-v1 adds emphasis on multi-scale thermal patterns, confidence scoring, and finite-difference/GMRES refinement.\n\n\n\nThat line of work is useful because it treats thermal simulation as an **operator learning** problem rather than just a generic regression problem.\n\n## Metrics I would not skip\n\nFor early design screening, field MSE alone is probably not enough.\n\nI would track:\n\nMetric | Why\n---|---\n**Mean / relative field error** | Basic global accuracy.\n**Max temperature error** | Often more important than average error in thermal design.\n**Hotspot location error** | A field can look good globally but miss the failure-relevant location.\n**Top-k hotspot recall** | Useful if you screen for dangerous regions.\n**Thermal resistance error** | More design-relevant than raw field error in many workflows.\n**Boundary flux / energy residual** | Helps detect physically inconsistent predictions.\n**Design ranking consistency** | If the surrogate is used for screening, preserving candidate ranking may matter more than absolute field accuracy.\n**OOD confidence / abstention rate** | A surrogate should know when not to be trusted.\n**Solver-refinement improvement** | If you use a hybrid ML+solver workflow, measure how much correction is needed.\n\nThe “where does accuracy actually break?” question should be answered by these slices, not just by one average error number.\n\n## Data strategy may matter as much as model class\n\nBecause full thermal solves are expensive, I would not only compare neural architectures. I would also design the data-generation loop.\n\nPossible additions:\n\nStrategy | Why it helps\n---|---\n**Multi-fidelity data** | Use cheaper approximate solves plus a smaller number of high-fidelity solves.\n**Active learning** | Spend expensive simulations where uncertainty or expected design value is highest.\n**Geometry-aware sampling** | Ensure training shapes cover topology/size/aspect-ratio regimes, not just random parameter values.\n**Boundary-condition sampling** | Sample BCs/source terms deliberately instead of treating them as afterthoughts.\n**Uncertainty estimation** | Needed for screening, especially under geometry shift.\n**Solver fallback / refinement** | Use ML as a fast initializer or screening model, not necessarily as the final authority.\n\nA slightly simpler model with a better data strategy can beat a more sophisticated model trained on a weak random split.\n\n## Suggested experiment matrix\n\nA practical comparison could look like this:\n\nTrack | Candidate | Purpose\n---|---|---\n**Baseline 0** | Classical surrogate: Gaussian process / random forest / gradient boosting on engineered geometry descriptors | Check whether deep learning is actually needed for your current design family.\n**Baseline 1** | 3D CNN / U-Net on voxel or SDF grid | Simple structured-grid baseline.\n**Baseline 2** | MeshGraphNet | Main unstructured-mesh baseline.\n**Baseline 3** | X-MeshGraphNet / multi-scale GNN | Large 3D / long-range / meshing-at-inference baseline.\n**Operator 1** | Geo-FNO | FNO-like model adapted to irregular geometry.\n**Operator 2** | GINO | Hybrid graph/Fourier neural operator for varying geometries.\n**Operator 3** | DeepOHeat / DeepONet-style model | Especially if the problem resembles chip/package thermal maps.\n**Physics hybrid** | PINO-style loss or weak-form residual added to the best supervised model | Test whether physics improves sample efficiency and OOD behavior.\n**Trust layer** | ensemble / confidence score / residual check / solver refinement | Test operational reliability.\n\nI would avoid spending too much time tuning every model before the validation protocol is stable. The first goal should be to find **which representation and split actually expose the failure modes**.\n\n## What I would ask in the Hugging Science Discord\n\nIf you ask there, I would include very concrete details. For example:\n\nDetail | Why people will ask\n---|---\nIs the geometry native CAD B-rep, STL, surface mesh, or volume mesh? | Determines representation and architecture.\nAre the outputs on volume nodes, surface nodes, voxels, or probe points? | Determines model output format.\nIs it conduction only, conjugate heat transfer, or CFD-coupled? | Changes physics and loss design.\nAre BCs simple scalars or spatial fields? | Determines whether operator learning is needed.\nHow many high-fidelity solves can you afford? | Determines whether deep models are realistic.\nAre materials fixed or variable? | Important for OOD splits.\nWhat is the design objective? | Max temperature, hotspot position, thermal resistance, ranking, etc.\nHow far outside training geometry should the model work? | Determines whether extrapolation is realistic.\nDo you need real-time prediction or just cheaper batch screening? | Changes acceptable model complexity.\n\nA compact prompt might be:\n\n> I am building a surrogate for steady-state thermal fields in electronics/battery design. Inputs are parameterized CAD geometry plus boundary conditions; labels are expensive CFD/thermal solves. Outputs are full temperature fields and hotspot-related quantities. I’m trying to choose between mesh-GNNs, geometry-aware neural operators, and PINN/PINO-style physics constraints. I would especially appreciate advice on representation choice, OOD geometry validation, and whether mesh-based GNNs or neural operators are more robust for this type of thermal problem.\n\n## Resource list\n\n### Mesh / graph simulation\n\n  * MeshGraphNets: Learning Mesh-Based Simulation with Graph Networks\n  * MeshGraphNets project page\n  * X-MeshGraphNet: Scalable Multi-Scale Graph Neural Networks for Physics Simulation\n  * PhysicsNeMo MeshGraphNet tutorial\n  * NVIDIA PhysicsNeMo GitHub\n\n\n\n### Geometry-aware neural operators\n\n  * Geo-FNO: Fourier Neural Operator with Learned Deformations for PDEs on General Geometries\n  * Geo-FNO arXiv\n  * GINO: Geometry-Informed Neural Operator for Large-Scale 3D PDEs\n  * GINO OpenReview\n  * DoMINO / PhysicsNeMo external aerodynamics example\n\n\n\n### Thermal / electronics operator learning\n\n  * DeepOHeat: Operator Learning-based Ultra-fast Thermal Simulation in 3D-IC Design\n  * DeepOHeat GitHub\n  * DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design\n\n\n\n### Physics-informed operator learning\n\n  * PINO: Physics-Informed Neural Operator for Learning Partial Differential Equations\n\n\n\n### CAD representation\n\n  * BRepNet: A topological message passing system for solid models\n  * BRepNet GitHub\n\n\n\n### Validation / distribution shift\n\n  * SIMSHIFT: A Benchmark for Adapting Neural Surrogates to Distribution Shifts\n  * REALM benchmark\n\n\n\n## Bottom line\n\nMy best reading from the public literature is:\n\n  * **If you have unstructured simulation meshes:** start with **MeshGraphNet / X-MeshGraphNet / graph neural operators**.\n  * **If you want FNO-like speed on irregular geometry:** use **Geo-FNO / GINO / DoMINO** , not vanilla FNO.\n  * **If the target is 3D-IC / chip-package thermal:** check **DeepOHeat / DeepONet / FNO-style thermal operator learning**.\n  * **If labels are scarce:** focus on **multi-fidelity data, active learning, physics-informed losses, and uncertainty**.\n  * **If reliability matters:** prioritize **OOD splits, hotspot metrics, confidence estimates, and solver refinement**.\n  * **If using PINNs:** use them mainly as **auxiliary physics constraints, inverse-calibration tools, or refinement mechanisms** , not as the default standalone surrogate.\n\n",
  "title": "Choosing a surrogate-model architecture to predict steady-state thermal fields from CAD geometry — FNO vs PINN vs GNN?"
}