HEATR is the coupled 2.5D/3D forward and inverse-design platform I built for RFAM. It connects a complex-coefficient electro-quasi-static field solve to generator-power-scaled RF deposition, transient heat transfer, DSC-calibrated phase change, and viscous-capillary densification. The same physics then runs in reverse: a finite-difference-verified adjoint computes how every printable dopant cell changes the final melted geometry, enabling the software to convert target parts into machine-ready material maps and exposure instructions.
See it in motion
A short field guide to HEATR — the electrothermal pipeline (field solve → RF power → melt → densification), then launching a run and reading the results.
HEATR field guide • loops automatically • drag the scrubber to review any moment
18/18
Printable solved maps beat uniform dopant
13/18
Beat the best stored map for each shape
7
Shapes clear the 0.95 IoU solved gate
From Geometry to Printer-Ready Compensation
The second-generation solver minimizes shape error directly, penalizing both unfused material inside the target and melt that escapes into the surrounding powder. One backward adjoint sweep returns the gradient for every dopant cell at roughly the cost of one forward solve. The pipeline jointly selects the dopant field and exposure stop, then filters and quantizes the result to the machine's 4-bit raster convention before re-running it through the production forward model.
Across the standardized 18-shape library, the printable single-pass map beat uniform dopant on all 18 shapes and the best stored historical map on 13. Seven shapes reached the absolute solved class of melt-region IoU ≥ 0.95. Four-bit quantization changed IoU by no more than 0.0035 across the census, showing that the optimized structure survives the transition from a continuous design variable to a printable instruction.
18-Shape Adjoint Design Census
Three-Dimensional Solved Map
The Geometry-Coupling Problem
In a parallel-plate RF field, energy coupling is not uniform. Corners and edges perpendicular to the applied field concentrate the E-field dramatically, while surfaces parallel to the field couple weakly. This means every different geometry produces a different heating pattern, and for non-symmetric shapes the results can be severe: one region of a part can be fully sintered while another barely reaches melt temperature. This is not a bug you can engineer away at the system level. It is an inherent feature of EQS heating. The only path forward is to understand the coupling for each geometry and develop compensation strategies that work around it. That requires a simulation tool fast enough to explore the space systematically.
Circle: Voltage, E-field & RF Heating
Square: Voltage, E-field & RF Heating
Why Build a Custom Solver?
COMSOL can assemble the same coupled physics, and it remains an independent reference for HEATR. The advantage is not an exaggerated single-solve speed claim: a comparable transient case takes roughly 30 seconds in HEATR versus 60–70 seconds in COMSOL. The decisive difference is throughput and control. HEATR carries no per-run meshing, GUI, or license-seat overhead, so hundreds of unattended geometry, orientation, grading, and adjoint evaluations are scriptable. Owning the forward model also makes it possible to embed custom densification endpoints, quantization gates, inverse-design objectives, and exact adjoints directly in the solve.
Current Design System
- Forward physics: Coupled EQS, RF power deposition, transient thermal transport, phase change, and densification in 2.5D and 3D.
- Adjoint material design: Shape-fidelity gradients for every dopant cell at approximately one additional forward-solve cost.
- Printability gates: Filtering, smoothing, 4-bit quantization, grid transfer, energy-residual checks, and production-forward re-evaluation.
- Additional actuators: Exposure stop, RF drive, orientation, asymmetric dwell, field averaging, and geometry pre-distortion.
- Method selection: Geometry-specific routing identifies where grading works and where field shadowing or power limits require another lever.
Forward + Adjoint Design Loop
Ungraded vs. Adjoint-Designed
Watch the Inverse Design Converge
The animation below contrasts a one-shot proportional inverse mask with the adjoint solve. Instead of inferring a correction from a proxy field, the adjoint repeatedly evaluates the printable dopant map through the coupled RF, thermal, and densification physics, driving the final melted geometry toward the target.
Hexagon: Proportional Inversion vs. Adjoint Solve
When Material Grading Is Not Enough
Some re-entrant and multi-lobed geometries remain limited by field shadowing or available power. HEATR can then search process actuators as well as material maps. These SFF 2026 animations show how rotation changes the heating kernel, how an indexed two-stage schedule melts an L-shape limb by limb, and how asymmetric dwell distributes energy across a cross. The results are simulation-established; the current electrode-medium contact architecture prevents physical turntable implementation without a hardware change.
Rotation Changes the Heating Kernel
Sequential L: Limb-by-Limb Exposure
Cross: Asymmetric Dwell Schedule
Verification, Cross-Checks & Open Validation
Every run reports field maps, thermal and densification histories, energy-balance residuals, and numerical diagnostics. The forward physics is cross-checked against COMSOL on reference cases, and a one-parameter calibration against a recovered independent IR transient reproduces the measured time-to-melt. The adjoint is verified against finite differences before optimization and satisfies the forward/adjoint transpose test to machine precision.
The remaining boundary is explicit: dedicated full-field validation on the current RFAM machine has not yet been completed, and the model still uses published 30 wt% graphite-in-nylon electrical data as a stand-in for the deployed 25 wt% carbon-black ink. Absolute heating magnitudes therefore remain model-relative pending impedance spectroscopy and closed-loop IR validation. The compensation results are simulation-established, not yet experimentally demonstrated.
Circle: Temperature, Melt & Density
Square: Temperature, Melt & Density
Optimizer: Convergence Report
Validation: Energy & Solver Diagnostics
Simulation Platform & GUI
HEATR includes a browser-based GUI for operational control and results exploration. The Operation page provides run configuration (geometry, mode, exposure, turntable parameters), a live job queue with real-time progress tracking, and inline simulation previews. The Results browser offers filterable run history with hero previews, expandable per-run metrics with contextual explanations, and quick access to all output figures. The platform also includes a Files tab for direct output browsing and a Theory tab with integrated physics reference documentation.
GUI: Operation & Job Queue
GUI: Results Browser
Technical Details
- Physics: Complex-coefficient electro-quasi-static field solve, generator-power-scaled RF deposition, transient thermal transport, DSC-calibrated apparent heat capacity, and viscous-capillary densification
- Models: Production 2.5D solver plus a volumetric 3D port for full build-height studies
- Inverse design: Direct/adjoint material optimization, exposure-stop selection, orientation, field averaging, and geometry pre-distortion
- Numerical gates: Finite-difference gradient checks, grid refinement and transfer checks, filtering, 4-bit quantization, energy residuals, and production-forward re-evaluation
- Stack: Python, NumPy, SciPy (sparse), Matplotlib, browser-based GUI with live job management
Electrothermal Simulation
RF Heating
Adjoint Inverse Design
Functionally Graded Materials
Shape Fidelity
Finite-Difference Verification
Python
