Stochastic reduced order models for inverse problems under uncertainty.

Area of Science:

• Computational mechanics
• Applied mathematics
• Uncertainty quantification

Background:

• Inverse problems are crucial for system identification but are often complicated by uncertainties.
• Existing methods struggle with efficiently handling probabilistic information and complex system dynamics.

Purpose of the Study:

• To develop a novel, efficient, and non-intrusive methodology for solving inverse problems under uncertainty.
• To leverage stochastic reduced order models (SROMs) for probabilistic parameter estimation.

Main Methods:

• Representing random quantities using low-dimensional, discrete SROMs.
• Transforming stochastic optimization problems into deterministic ones via SROM characterization.
• Utilizing non-intrusive gradient computations with existing deterministic solvers.

Main Results:

• Successfully demonstrated the recovery of random shear moduli in elastodynamics using displacement statistics.
• Showcased the framework's effectiveness even when system loading is also random.
• Validated the method's ability to handle multiple sources of uncertainty.

Conclusions:

• The proposed SROM framework offers a widely applicable and efficient solution for inverse problems with uncertainty.
• This approach facilitates robust parameter estimation in complex systems like elastodynamics.
• The non-intrusive nature allows seamless integration with existing computational tools.