This project analyzes the Sampling Where It Matters (SWIM) framework [2], an innovative approach for training fully-connected neural networks that avoids iterative, gradient-based optimization by directly sampling weights from the available data.
The project explores the efficiency and versatility of the SWIM algorithm. The main objective is to overcome the computational bottlenecks of traditional backpropagation through a non-iterative, data-driven sampling strategy [2]. The analysis is structured into two main phases:
- Multi-Fidelity Regression: Application of SWIM to multi-fidelity problems, where the framework is used to approximate the benchmark Forrester function.
- Physics-Informed Modeling (SWIM-PDE): By incorporating physical constraints directly into the network architecture, SWIM-PDE [1] provides a fast alternative to traditional Physics-Informed Neural Networks (PINNs). Within this framework, the performance of SWIM-PDE is evaluated and compared to PINNs specifically for the reconstruction of heartbeat propagation via the Eikonal equation.
- [1] C. Datar et al. "Solving partial differential equations with sampled neural networks", arXiv:2405.20836, 2024.
- [2] E. Bolager et al. "Sampling weights of deep neural networks", NeurIPS 2023; arXiv:2306.16830.
This repository adopts a dual-licensing approach to distinguish between the software components and the scientific documentation:
The source code and scripts in this repository are licensed under the MIT License. Since this implementation builds upon existing frameworks and external libraries, you are free to use, modify, and distribute the code, provided that the original license and copyright notice are included.
The project report (SWIM_Scientific_Report.pdf) and the visual results are protected. All rights are reserved to the authors: Arianna Cagali, Mattia Gastoldi, and Roberto Gastoldi.
- Non-Manipulable: You are not allowed to modify, alter, or build upon the report text or the visual results for further distribution.
- Non-Commercial: The use of the report, findings, or posters for profit is strictly prohibited.
- Attribution: You are free to download and share the report for personal or academic purposes, provided that appropriate credit is given to the original authors.
For questions, clarifications, or further information about the project, feel free to contact me at mattia.gastoldi@mail.polimi.it or roberto.gastoldi@mail.polimi.it. Upon request, further details can be provided.