Improving reduced-order models through nonlinear decoding of projection-dependent outputs.

Area of Science:

• Computational science
• Data science
• Machine learning

Background:

• Data-driven reduced-order models (ROMs) are crucial for simulating complex dynamical systems.
• Poor topological quality in low-dimensional data projections hinders ROM accuracy, causing issues like overlapping, twisting, and steep gradients in quantities of interest (QoIs).

Purpose of the Study:

• To introduce a novel dimensionality reduction technique using encoder-decoder neural networks.
• To improve the topological quality of low-dimensional data projections for enhanced ROM performance.
• To minimize nonuniqueness and gradients in QoI representations within the reduced dimension.

Main Methods:

• Employing an encoder-decoder neural network architecture for dimensionality reduction.
• Utilizing nonlinear decoding of projection-dependent QoIs to embed them within the dimensionality reduction process.
• Linking data projection (encoding) accuracy to the nonlinear reconstruction of QoIs (decoding).

Main Results:

• Achieved improved low-dimensional representations for complex multiscale and multiphysics datasets.
• Minimized nonuniqueness and gradients in the representation of QoIs on the projection.
• Demonstrated enhanced predictive accuracy of the resulting reduced-order models.

Conclusions:

• Nonlinear decoding of QoIs within dimensionality reduction significantly improves data representations.
• This approach enhances the predictive capabilities of data-driven ROMs for complex dynamical systems.
• The findings have broad applicability in fields like fluid dynamics, plasma physics, and neuroscience.