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Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
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Generative adversarial reduced order modelling.

Dario Coscia1, Nicola Demo1, Gianluigi Rozza2

  • 1Mathematics Area, mathLab, SISSA, via Bonomea 265, I-34136, Trieste, Italy.

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|February 16, 2024
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Summary
This summary is machine-generated.

We introduce GAROM, a novel generative adversarial model (GAM) for reduced-order modeling (ROM). This data-driven approach effectively learns solutions to parametric differential equations, enhancing model approximation capabilities.

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Area of Science:

  • Computational Science
  • Machine Learning
  • Numerical Analysis

Background:

  • Reduced-order modeling (ROM) approximates high-fidelity models with simpler ones.
  • Generative Adversarial Networks (GANs) learn data distributions using generator and discriminator networks.
  • GAN applications in ROM are underexplored.

Purpose of the Study:

  • To introduce GAROM, a novel generative adversarial model (GAM) for ROM.
  • To develop a data-driven approach for learning solutions to parametric differential equations.
  • To integrate GANs and ROM frameworks for enhanced model approximation.

Main Methods:

  • The discriminator is implemented as an autoencoder for feature extraction.
  • A conditioning mechanism is applied to generator and discriminator networks.
  • The methodology learns solutions to parametric differential equations.

Main Results:

  • Experimental evidence demonstrates the model's generalization capabilities.
  • A convergence study validates the method's performance.
  • The approach is applicable for inference tasks.

Conclusions:

  • GAROM offers a new data-driven method for ROM.
  • The model effectively learns solutions for parametric differential equations.
  • The approach shows promise for approximating complex systems.