The paper introduces a method based on Continuous Low Rank Adaptation (CoLoRA) that trains neural networks to predict the evolution of solution fields at new initial conditions and physics parameters. The method can adapt purely data-driven or via an equation-driven variational approach. CoLoRA approximates solution fields locally in time, requiring only a few training trajectories offline, making it suitable for data-scarce regimes. Predictions with CoLoRA are significantly faster and more accurate compared to other neural network approaches. The paper also discusses the concept of the Kolmogorov barrier and how CoLoRA can bypass it.


Publication date: 23 Feb 2024
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