Enhancing Symbolic Regression and Universal Physics-Informed Neural Networks with Dimensional Analysis

We present a new method for enhancing symbolic regression for differential equations via dimensional analysis, specifically Ipsen's and Buckingham pi methods. Since symbolic regression often suffers from high computational costs and overfitting, non-dimensionalizing datasets reduces the number of input variables, simplifies the search space, and ensures that derived equations are physically meaningful. As our main contribution, we integrate Ipsen's method of dimensional analysis with Universal Physics-Informed Neural Networks. We also combine dimensional analysis with the AI Feynman symbolic regression algorithm to show that dimensional analysis significantly improves the accuracy of the recovered equation. The results demonstrate that transforming data into a dimensionless form significantly decreases computation time and improves accuracy of the recovered hidden term. For algebraic equations, using the Buckingham pi theorem reduced complexity, allowing the AI Feynman model to converge faster with fewer data points and lower error rates. For differential equations, Ipsen's method was combined with Universal Physics-Informed Neural Networks (UPINNs) to identify hidden terms more effectively. These findings suggest that integrating dimensional analysis with symbolic regression can significantly lower computational costs, enhance model interpretability, and increase accuracy, providing a robust framework for automated discovery of governing equations in complex systems when data is limited.

A Novel Approach to Image EEG Sleep Data for Improving Quality of Life in Patients Suffering From Brain Injuries Using DreamDiffusion

Those experiencing strokes, traumatic brain injuries, and drug complications can often end up hospitalized and diagnosed with coma or locked-in syndrome. Such mental impediments can permanently alter the neurological pathways in work and significantly decrease the quality of life (QoL). It is critical to translate brain signals into images to gain a deeper understanding of the thoughts of a comatose patient. Traditionally, brain signals collected by an EEG could only be translated into text, but with the novel method of an open-source model available on GitHub, DreamDiffusion can be used to convert brain waves into images directly. DreamDiffusion works by extracting features from EEG signals and then using the features to create images through StableDiffusion. Upon this, we made further improvements that could make StableDiffusion the forerunner technology in waves to media translation. In our study, we begin by modifying the existing DreamDiffusion codebase so that it does not require any prior setup, avoiding any confusing steps needed to run the model from GitHub. For many researchers, the incomplete setup process, errors in the existing code, and a lack of directions made it nearly impossible to run, not even considering the model's performance. We brought the code into Google Colab so users could run and evaluate problems cell-by-cell, eliminating the specific file and repository dependencies. We also provided the original training data file so users do not need to purchase the necessary computing power to train the model from the given dataset. The second change is utilizing the mutability of the code and optimizing the model so it can be used to generate images from other given inputs, such as sleep data. Additionally, the affordability of EEG technology allows for global dissemination and creates the opportunity for those who want to work on the shared DreamDiffusion model.