Leonard Gleyzer

Varun Kumar, Leonard Gleyzer, Adar Kahana et al.

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 MyCrunchGPT, 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 MyCrunchGPT 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 MyCrunchGPT, 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 MyCrunchGPT 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.

Adar Kahana, Qian Zhang, Leonard Gleyzer et al.

The main computational task of Scientific Machine Learning (SciML) is function regression, required both for inputs as well as outputs of a simulation. Physics-Informed Neural Networks (PINNs) and neural operators (such as DeepONet) have been very effective in solving Partial Differential Equations (PDEs), but they tax computational resources heavily and cannot be readily adopted for edge computing. Here, we address this issue by considering Spiking Neural Networks (SNNs), which have shown promise in reducing energy consumption by two orders of magnitude or more. We present a 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 first propose a new method for encoding continuous values into spikes based on a triangular matrix in space and time, and demonstrate its better performance compared to the existing methods. Next, we demonstrate that using a simple SNN architecture consisting of Leaky Integrate and Fire (LIF) activation and two dense layers, we can achieve relatively accurate function regression results. Moreover, we can replace the LIF with a trained Multi-Layer Perceptron (MLP) network and obtain comparable results but three times faster. Then, we introduce the DeepONet, consisting of a branch (typically a Fully-connected Neural Network, FNN) for inputs and a trunk (also a FNN) for outputs. We can build a spiking DeepONet by either replacing the branch or the trunk by a SNN. We demonstrate this new approach for classification using the SNN in the branch, achieving results comparable to the literature. Finally, we design a spiking DeepONet for regression by replacing its trunk with a SNN, and achieve good accuracy for approximating functions as well as inferring solutions of differential equations.