AI-native thermal physics for microelectronics

Thermal physics beyond the Fourier era.

The first GPU-native multiscale non-Fourier thermal model, from transistor to chip, and the only one differentiable end-to-end to enable gradient-based design optimization.

Patent PendingNotre DameDARPA-funded
  • 90 °C
    Underprediction by Fourier-based model on nanotransistor hotspot
  • 1st
    Fully differentiable multiscale thermal model
  • 10⁸×
    Speed up for large transistor array simulation
  • 100M DoF
    Largest single-GPU phonon BTE simulation ever run

Why Fourier breaks

In nano-transistors, the heat equation is not just wrong — it's wrong by tens of degrees.

Below the phonon mean free path, ballistic transport dominates and Fourier's law breaks down. Commercial EDA thermal tools — built on Fourier — can underpredict peak nano-transistor temperatures by up to 90 °C. They predict barely any heat up where the physics yields 124 °C. That's the difference between a chip that runs and a chip that fails.

Fourier (commercial EDA): peak temperature 308 K
Fourier (commercial EDA)
308 K
JAX-BTE (phonon physics): peak temperature 398 K
JAX-BTE (phonon physics)
398 K

Peak temperature, identical FinFET-array geometry. Difference: 90 K.

How it works

One solver. One surrogate. One coupling. End-to-end differentiable.

Three pillars work together so you get ground-truth phonon physics in the transistor, millisecond inference for design loops, and chip-scale assemblies in one continuous pipeline.

  • Differentiable BTE solver

    01

    GPU-native FVM solver for the non-gray phonon Boltzmann Transport Equation. Discrete ordinates, BiCGSTAB inner solves, automatic differentiation end-to-end — forward and inverse, both.

    • Up to 100M DoF on a single A100
    • JAX-native
    • First-of-its-kind inverse design
  • Neural field surrogates

    02

    FinNET and SOLDER — operator-learning surrogates trained on JAX-BTE ground truth. Millisecond inference at 95–99% BTE accuracy. Training in under 30 minutes on a single GPU.

    • CP-decomposed conditioning
    • Sub-millisecond inference
    • 30-minute training
  • Multiscale Fourier–BTE coupling

    03

    Overlapping domain decomposition: BTE-accurate solves in transistor regions (Kn ≥ 1) coupled to Fourier solvers in substrate regions. 7× speedup, 74% memory reduction, sub-1 K error.

    • 7× speedup vs full BTE
    • 74% memory reduction
    • Sub-1 K error

Interactive · 360,000 transistors

Explore a die at six zoom levels.

Drive in from a 360,000-transistor overview to the internal mechanics of a single FinFET. Drag the heat source slider to see the thermal field respond. Built on the same JAX-BTE-trained surrogates we ship to customers.

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Receipts

Peer-reviewed. Patent-pending. Federally funded.

  • Published

    npj Comput. Mater. 11:129 (2025)

    Peer-reviewed validation in Nature Portfolio — convergence, FinFET arrays, inverse recovery, all benchmarked.

    Read the paper ↗
  • Patented

    Patent Pending (PCT/US25/36027)

    Tensor-based parallel BTE execution, differentiable inverse design, multiscale coupling — protected end-to-end.

  • Funded

    DARPA · NSF

    Supported by DARPA Thermonat Program and the NSF FUSE2 Program.

Discovery

What semiconductor thermal teams told us.

We talked to thermal engineers at the top foundries and the largest fabless designers. They told us where the gaps are.

  • 3D IC thermo-mechanical modeling is a gold mine — there are no good existing models.
    Thermal simulation lead, leading foundry
  • A differentiable thermal solver would be fantastic for design optimization. Current tools are impractical at optimization scale.
    Multi-physics simulation engineer, leading foundry
  • Reduced-order thermal models take two hours per chip. We'd value a tool like this in the tens of millions.
    Package thermal engineer, fabless leader

Quotes anonymized; pending permission for attribution.