Neural Network Surrogate for Thermal Protection System Design

Implement a 1D transient heat conduction solver using the finite difference method (or finite element method) in Python. The domain is a multi-layer stack: outer TPS material (e.g., PICA, SLA-561V, or AVCOAT), an insulation layer (e.g., LI-900 or Saffil), a structural subpanel (aluminum or composite), and internal air/structure. Discretize each layer into 10–20 elements with finer mesh near material interfaces.

Use the Crank-Nicolson implicit scheme for time integration (unconditionally stable). Implement temperature-dependent thermal conductivity and specific heat for each material using polynomial fits from published data (NASA TPS material property databases). At the outer surface, apply a heat flux boundary condition (from the reentry trajectory) minus re-radiation (sigma * epsilon * T^4). At the inner surface, apply an adiabatic condition or a fixed-temperature structural sink. Validate against published benchmark problems — the TPSX database from NASA Ames provides reference solutions for standard TPS stackups.

Identify the design parameters to vary: outer TPS layer thickness (1–8 cm), insulation layer thickness (1–5 cm), outer material type (3–4 options: PICA, SLA-561V, AVCOAT, LI-2200), insulation material type (2–3 options: LI-900, Saffil, aerogel), bond line conductance (representing adhesive quality: 50–500 W/m2-K), and reentry trajectory parameters that define the heat flux profile: peak heat flux (50–500 W/cm2), total heat load (5,000–50,000 J/cm2), and trajectory duration (100–600 seconds).

Parameterize the reentry heat flux as a Chapman-type profile: q(t) = q_peak * sin(pi*t/t_total)^n, where n controls the profile shape. This two-parameter family (peak + duration) covers a wide range of realistic reentry trajectories from LEO return to lunar return. Use Latin Hypercube Sampling to generate 10,000–20,000 parameter combinations.

Run the thermal solver for each parameter combination. For each case, extract the output data: temperature vs. time at each material interface (outer surface, TPS/insulation interface, insulation/structure interface, inner surface). Also extract key scalar outputs: peak bondline temperature (the critical design metric — adhesive fails above ~260 degC), peak structural temperature, time to peak structural temperature (it occurs after the heating pulse due to thermal lag), and total heat absorbed by each layer.

Store the dataset efficiently: input parameters as a feature matrix, temperature histories as a 3D array (samples x interfaces x time steps), and scalar outputs separately. Use HDF5 via h5py for compact storage. Generation will take several hours — parallelize with Python's concurrent.futures across CPU cores. Sanity-check results: verify energy conservation (total heat input equals sum of stored energy plus re-radiated energy to within 1%).

Build a multi-output feed-forward neural network in PyTorch. The input is a vector of design parameters (material indices encoded as learned embeddings, thicknesses, bond conductance, trajectory parameters). The output predicts both scalar quantities (peak bondline temperature, peak structural temperature) and optionally the full temperature time history at each interface.

For the scalar predictions, use a network with 4–5 hidden layers (256-512-256-128-64 units), batch normalization, and GELU activations. For full time-history prediction, use a hypernetwork approach: the design parameters produce weights for a small network that maps time to temperature, or use a decoder architecture that maps the design parameter embedding to a sequence of temperature values. Train with MSE loss, but add a penalty term for underestimating peak bondline temperature — this is the safety-critical output where conservative predictions are essential.

Split data 80/10/10 into train/validation/test. Train with Adam optimizer (lr=1e-3, weight decay=1e-5), batch size 512, for 200–300 epochs with cosine annealing and early stopping on validation loss. Monitor training with TensorBoard or Weights & Biases.

Benchmark the surrogate: compute prediction time vs. FEA simulation time. The neural network should predict in under 1 millisecond per case, compared to 10–60 seconds for the FEA solver — a speedup of 10,000–100,000x. Report accuracy as RMSE and maximum error on the test set for each output quantity. The critical question: is the maximum error on peak bondline temperature small enough for design decisions? Aim for max error below 10 degC (compared to the ~260 degC limit).

Use the trained surrogate for rapid design exploration. Sweep TPS thickness from 1 to 8 cm and plot peak bondline temperature — you'll see the expected monotonic decrease (more insulation = lower structural temperature) with diminishing returns at large thicknesses. Create 2D contour plots showing peak bondline temperature as a function of two design variables (e.g., TPS thickness vs. insulation thickness) for different reentry severities.

Identify the minimum-weight TPS stackup that keeps bondline temperature below 260 degC for a given reentry trajectory. Use scipy's minimize with the surrogate as the objective function — because the surrogate evaluates in microseconds, this optimization completes in seconds. Compare the optimal design with the known solution from parametric FEA sweeps. Perform the same optimization for 3–4 different reentry trajectories and show how the optimal design changes.

Quantify the surrogate's uncertainty using ensemble methods: train 5 networks with different random seeds and use the prediction variance as an uncertainty estimate. Map the uncertainty across the design space — it should be highest near the training data boundaries (extrapolation) and in regions where the physics is most non-linear (near ablation onset, near material phase transitions).

Write a research-quality report. Discuss the limitations of the 1D thermal model (real TPS has 2D/3D effects, gap heating, surface catalysis) and how these affect the surrogate's applicability. Address the path from surrogate model to engineering tool: what additional validation against flight data, arc jet testing, or high-fidelity 3D CFD/thermal simulation would be needed before using the surrogate for preliminary design decisions? Reference current NASA and SpaceX approaches to TPS design and where ML surrogates fit in the workflow.