Differentiable physics at 10⁻¹⁴ precision
The Axiom Engine turns stiff industrial PDEs into mathematically certain, physically grounded solutions. KenCarp4 IMEX stepping, SIREN neural layers, and strict Jacobian verification let teams solve in minutes without sacrificing fidelity.
KenCarp4 IMEX Solvers
Implicit-explicit time stepping tuned for stiff reaction-diffusion systems and industrial transport dynamics.
SIREN Neural Layers
Sinusoidal activations capture sharp gradients and multi-scale coupling without spectral bias or instability.
Max Diff = 0.0
Bitwise deterministic solver trajectories across matched runs — no stochastic drift, only physical consistency.
Glass-Box Physical Traceability
Every result is bound to an interpretable governing equation, making the workflow auditable for enterprise deployment.
O(1) Memory. Infinite depth.
Laminar-GND replaces dense graph convolutions with continuous reaction-diffusion dynamics. The Adjoint Sensitivity Method lets the model scale to industrial cartography without the memory wall of traditional deep networks.
Adjoint Sensitivity Method
Backpropagation through the differential equation rather than the full activation graph, allowing O(1) Memory with respect to solver depth.
BCOO Sparse Format
The graph Laplacian is represented as a blocked sparse operator, avoiding dense materialization while preserving high-fidelity resolution.
Zero Over-Smoothing
Reaction-diffusion balancing prevents the collapse that plagues deep graph networks and preserves high-frequency physical structure.
Architecture comparison
| Architecture | Temporal | Spatial Operator | Memory | Over-smoothing |
|---|---|---|---|---|
| Standard GCN | Discrete | Adjacency Matrix | O(L·N·F) | High |
| Transformer (ViT) | Discrete | Dense Self-Attention | O(L·N²) | Moderate |
| Laminar-GND | Continuous | BCOO Sparse Laplacian | O(1) with Depth | Zero |
Quantum-native simulation. Zero-trust data architecture.
The same continuous JAX/XLA substrate used for industrial physics maps natively onto quantum-accelerated workloads, while our encrypted pipeline protects proprietary process data end-to-end.
TenSEAL CKKS
We encrypt proprietary solver inputs and telemetry before execution. Divergence remains at ~9.5 × 10⁻⁷, preserving physical integrity without exposing sensitive process data.
Quantum Key Distribution
Our continuous optimization stack is designed to exploit secure quantum networking and QKD-era transport layers, delivering a >6,000x optimization speedup across protected high-value workloads.
Constrained MAS with machine-traceable AI
LLM agents handle workflow routing, but every recommended action is validated against concrete data contracts before it reaches the solver stack.
Agent-Based Routing
Specialized LLM agents parse CAD, subsystem metadata, and system telemetry without uncontrolled autonomy.
Schema-Bound Execution
Every agent output is enforced against a typed data contract before any physics computation begins.
Human-in-the-Loop Control
Critical decisions are gated, reviewed, and traceable for enterprise-critical infrastructure and mission-critical workflows.
Ready to benchmark the physics stack?
We build targeted technical demos for qualified enterprise, aerospace, and quantum infrastructure partners.
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