Paramatrized intrusive POD-based reduced-order models applied to advection-diffusion-reaction problems.

Area of Science:

• Computational Science and Engineering
• Numerical Analysis
• Scientific Computing

Background:

• Parametrized problems often require significant computational resources when solved using traditional numerical methods.
• Reduced-order models (ROMs) offer a computationally efficient alternative for solving such problems.
• Proper Orthogonal Decomposition (POD) is a key technique for constructing ROMs.

Purpose of the Study:

• To investigate methods for extending the capabilities of ROMs beyond the limits imposed by their training datasets.
• To explore strategies for obtaining accurate solutions for a wider range of parameters in complex problems.
• To demonstrate the practical application of these methods using relevant numerical models.

Main Methods:

• Utilizing Proper Orthogonal Decomposition (POD) to build reduced-order models.
• Developing techniques to overcome computational limitations inherent in ROM training sets.
• Applying and validating the proposed methods on the 2D advection-diffusion-reaction equation.
• Testing the approach on a 2D wildfire propagation model.

Main Results:

• Demonstrated that ROMs significantly reduce computational cost for parametrized problems.
• Identified and explored strategies to surpass the computational boundaries set by ROM training data.
• Successfully applied the enhanced ROM techniques to both the advection-diffusion-reaction and wildfire models.
• Achieved accurate solutions for problems with varying parameters, overcoming initial ROM limitations.

Conclusions:

• ROMs, particularly those based on POD, provide a powerful and efficient approach for solving parametrized problems.
• The explored methods effectively extend the applicability of ROMs, enabling solutions beyond initial training set constraints.
• The successful application to complex models like wildfire propagation highlights the practical utility of these advanced ROM techniques.