Scientific Computing

Accelerate Scientific Computing with AAD

Speed up PDEs, optimization methods, and regressions by 6-100x using state-of-the-art automatic adjoint differentiation. With MatLogica, you save development time and reduce execution costs for large-scale scientific applications.

Focus on Science, Not Optimization

Our software allows scientists and engineers to focus on mathematical problems rather than performance optimization, achieving better performance and calculating adjoints automatically without manual derivative coding.

6-100x Faster

Than manual adjoint implementation or finite differences

Automatic Gradients

No hand-coding required for derivatives

Million+ DOF

Handle massive finite difference/element grids efficiently

Core Capabilities

Gradient-Based Optimization

Automatically calculate the full Jacobian at a fraction of the usual computational cost. Essential for inverse problems, parameter estimation, and large-scale optimization in scientific computing.

Large-Scale PDE Sensitivity

MatLogica's AADC processes extremely large finite difference PDE schemes efficiently. It executes back-propagation quickly and flawlessly, computing sensitivities of PDE solutions relative to coefficients, boundary conditions, or initial data.

Automatic Adjoint Generation

No manual derivative coding required. AADC automatically generates efficient adjoint code for your PDE solvers, optimization routines, and regression models.

Applications Across Scientific Domains

Geophysics & Seismology

  • Full Waveform Inversion (FWI): Compute gradients for velocity model updates
  • Seismic Imaging: Sensitivity analysis for subsurface parameters
  • Reservoir Simulation: History matching and parameter estimation
  • Gravity/Magnetic Inversion: Fast gradient computation for geophysical inversions

Computational Fluid Dynamics

  • Shape Optimization: Aerodynamic design with gradient-based methods
  • Adjoint Flow Solvers: Navier-Stokes sensitivity analysis
  • Heat Transfer: Thermal optimization and inverse problems
  • Multiphase Flow: Parameter identification in complex flows

Weather & Climate Modeling

  • 4D-Var Data Assimilation: Efficient gradient computation for atmospheric models
  • Weather Forecasting: Adjoint sensitivity for initial conditions
  • Ocean Modeling: Parameter estimation in circulation models
  • Climate Sensitivity: Compute sensitivities to forcing parameters

Medical & Biomedical

  • Electric Impedance Tomography (EIT): Fast inverse problem solution
  • MRI Reconstruction: Gradient-based image optimization
  • Diffusion Imaging: Parameter estimation in tissue models
  • Biomechanics: Material property identification

Electromagnetics

  • Antenna Design: Shape optimization using adjoint methods
  • Scattering Problems: Inverse electromagnetic problems
  • Photonics: Device optimization with Maxwell solvers
  • Radar Imaging: Gradient-based reconstruction

Materials & Structures

  • Topology Optimization: Structural design with gradients
  • Material Identification: Inverse problems in mechanics
  • Composite Design: Multi-scale optimization
  • Fracture Mechanics: Parameter sensitivity analysis

Accelerate Your Scientific Computing

Let us benchmark AADC on your PDE solver or optimization problem