CrunchGPT: A chatGPT assisted framework for scientific machine learning

Scientific Machine Learning (SciML) has advanced recently across many different areas in computational science and engineering. The objective is to integrate data and physics seamlessly without the need of employing elaborate and computationally taxing data assimilation schemes. However, preprocessing, problem formulation, code generation, postprocessing and analysis are still time consuming and may prevent SciML from wide applicability in industrial applications and in digital twin frameworks. Here, we integrate the various stages of SciML under the umbrella of ChatGPT, to formulate CrunchGPT, which plays the role of a conductor orchestrating the entire workflow of SciML based on simple prompts by the user. Specifically, we present two examples that demonstrate the potential use of CrunchGPT in optimizing airfoils in aerodynamics, and in obtaining flow fields in various geometries in interactive mode, with emphasis on the validation stage. To demonstrate the flow of the CrunchGPT, and create an infrastructure that can facilitate a broader vision, we built a webapp based guided user interface, that includes options for a comprehensive summary report. The overall objective is to extend CrunchGPT to handle diverse problems in computational mechanics, design, optimization and controls, and general scientific computing tasks involved in SciML, hence using it as a research assistant tool but also as an educational tool. While here the examples focus in fluid mechanics, future versions will target solid mechanics and materials science, geophysics, systems biology and bioinformatics.

Function Regression using Spiking DeepONet

One of the main broad applications of deep learning is function regression. However, despite their demonstrated accuracy and robustness, modern neural network architectures require heavy computational resources to train. One method to mitigate or even resolve this inefficiency has been to draw further inspiration from the brain and reformulate the learning process in a more biologically-plausible way, developing what are known as Spiking Neural Networks (SNNs), which have been gaining traction in recent years. In this paper we present an SNN-based method to perform regression, which has been a challenge due to the inherent difficulty in representing a function's input domain and continuous output values as spikes. We use a DeepONet - neural network designed to learn operators - to learn the behavior of spikes. Then, we use this approach to do function regression. We propose several methods to use a DeepONet in the spiking framework, and present accuracy and training time for different benchmarks.