Machine Learning Research

Overview

In May 2024, I proactively joined Dr. Fuhg’s research group at the University of Texas to contribute to ongoing studies in Scientific Machine Learning, Computational Mechanics, Solid Mechanics, and Scientific Computing. Dr. Fuhg’s research is dedicated to developing data-driven computational science methodologies, particularly in modeling and forecasting the mechanics of materials across different length and time scales. His work also involves reliability analysis, uncertainty quantification, and the design of experiments.

Research Contribiton: My first assigned task was to replicate the findings of the paper Constrained Monotonic Neural Networks. The paper addresses the need for explainable AI by incorporating monotonicity constraints in neural networks, ensuring their reliability in critical fields such as finance and healthcare.

I successfully replicated the results of the paper while also converting the original codebase from TensorFlow to PyTorch, the preferred framework in our research group. My implementation demonstrated the ability to enforce monotonicity when applied to a simple function like , while failing to fit non-monotonic functions such as , validating the constraints imposed by the network.

Key Takeaways

• Gained hands-on experience in implementing and validating monotonic neural networks.

• Developed a deeper understanding of monotonicity constraints and their implications in neural network architecture.

• Strengthened my proficiency in PyTorch by translating and optimizing TensorFlow code.

• Contributed to the broader goal of creating reliable and interpretable machine learning models for scientific applications.

This research has provided me with valuable insights into the intersection of machine learning and computational mechanics, reinforcing my interest in developing AI-driven solutions for complex engineering problems.

The graphs above show the model is working in accurately predicting the function while enforcing a monotonic constraint. 

Whats Next? 

Following the successful replication of the Constrained Monotonic Neural Network, my next task is to extend this approach to polyconvex neural networks, ensuring that the learned models always produce positive outputs. Polyconvexity is a critical constraint in material modeling as it guarantees thermodynamic consistency and ensures the stability of hyperelastic material models. This aspect is particularly important for our work on modeling thermoelastic materials, where enforcing polyconvexity helps maintain well-behaved stress-strain relationships and enhances generalization capabilities of the model.