The Brillance of Ingenuity


CFD Research uses model order reduction (MOR) to develop reduced order models (ROMs). CFD Research’s MOR methodology is based on mathematically rigorous approaches (as opposed to empirical, analytical, or hardware-based methods), therefore it can used for real-time simulations on lesser machines without compromising accuracy or resolution. The methodology has been demonstrated and validated for diverse applications include aerospace, missile defense, energy, materials and biomedical.



  • Multi-physics modeling and simulation without compromising accuracy or resolution
  • Low-dimensional (compact) models extracted from full models for real-time systems and analyses
  • “Full-field” experimental & computational data reconstruction



  • Real-time simulation with up to 5 orders-of-magnitude speed-up
  • Accurate analysis with less than 2% error (typical)
  • Efficient optimization and robust control of complex systems
  • Quickly identify Regions of Interest (ROIs) for detailed analysis
  • Increased understanding of underlying physics
  • Provide guidance on reconfiguration of the multi-physics model


Equation Based Approach

Example: NASA X-56A Reduced-Order Models for controller design

Reduced states from 180 to 21

Negligible Error

"This technology will markedly reduce the development cycles of aerospace vehicles at reduced costs. It is inherently time- and parameter-varying by design to allow more intuitive analysis" - Marty Brenner, Aerospace Engineer at NASA Armstrong Flight Research Center

Data-Driven Approach

Example: AeroServoElastic (ASE) analysis of control fin

Aerodynamic ROM and Structural ROM coupled for integrated analysis

Relative Error < 2.5%, ~55,000x Speed-up


Example: Plasma Processing

180,000x speedup over CFD-ACE+ with Relative Error < 0.5%


Example: Radiation in a Semiconductor CVD Chamber

Full Model


3,300x speedup over Full Model with Relative Error < 1%