From Unsolved Problems to Production-Grade Solutions
Novel Problems Require Novel Approaches
Most engineering problems have established models. Navier-Stokes for fluid flow, linear elasticity for structures, Fourier's law for heat transfer. The simulation industry exists to solve these known equations faster and at higher fidelity. Some problems have no textbook model. The physics is novel, the coupling is unprecedented, or the phenomenon operates at scales where existing theory breaks down.
We work at that frontier, turning open mathematical questions into production-grade computational tools. That takes the mathematical maturity to formulate new models, the numerical analysis to discretize and solve them reliably, and the software engineering to make them run at industrial scale.
What We Help Solve
Problems that fall into the gap between academic research and industrial engineering:
Your Problem Has No Existing Model
The physics is novel or the coupling is unprecedented, so it needs an original mathematical formulation rather than a better implementation of an existing method
Standard Numerical Methods Don't Converge or Scale
Existing discretization approaches fail on your problem, so you need new numerical schemes, stabilization techniques, or solver architectures
AI That Must Respect Physical Laws
You need machine learning models that respect conservation laws when they extrapolate
Research Results Need to Become Production Algorithms
Academic papers demonstrate feasibility but the gap to reliable, deployable computational tools remains unbridged
OUR CAPABILITIES
The mathematical and computational science foundations behind every solution we deliver.
Building mathematical representations of physical systems directly from the governing laws.
Continuum mechanics, thermodynamics, and transport phenomena formulations
Multiscale modeling bridging molecular, mesoscale, and continuum descriptions
Inverse problem formulations for parameter identification and design
Mathematical modeling of emergent phenomena in complex systems
Designing, analyzing, and implementing numerical schemes with rigorous convergence guarantees.
Finite element, finite volume, and spectral method design and analysis
Stabilization techniques for advection-dominated and saddle-point problems
Multigrid methods and efficient iterative solvers for large-scale systems
Adaptive mesh refinement and error estimation strategies
Finding optimal designs under physical constraints, exploring design spaces that would take months to navigate by hand.
Adjoint-based gradient computation for efficient high-dimensional optimization
Shape and topology optimization under PDE constraints
Multi-objective optimization under competing physical objectives
Applications spanning aerodynamics, antenna design, structural mechanics, and biomedical engineering
AI architectures that embed physical structure, producing models that are explainable by mathematical construction.
Neural ODEs and dynamical systems approaches to deep learning
Multigrid methods for neural network training with convergence guarantees
Physics-constrained loss functions and architectures that respect conservation laws
Foundation model research for engineering simulation acceleration
Working on a Problem That Doesn't Have a Model Yet?
We build the mathematics and algorithms that turn open scientific questions into working computational tools.