# Energy Optimized Piecewise Polynomial Approximation Utilizing Modern Machine Learning Optimizers

arXiv: https://arxiv.org/abs/2503.09329 · HTML: https://mlsanity.com/paper/2503.09329/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 5 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 2 of 2)

- [Ck-continuous Spline Approximation with TensorFlow Gradient Descent Optimizers](https://mlsanity.com/paper/2303.12454/) (2023)
- [Machine Learning Optimized Orthogonal Basis Piecewise Polynomial Approximation](https://mlsanity.com/paper/2403.08579/) (2024)

## Abstract (arXiv)

This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets but lack flexibility in accommodating complex optimization goals. By leveraging modern gradient descent optimizers within TensorFlow, we introduce a framework that minimizes elastic strain energy in cam profiles, leading to smoother motion. Experimental results confirm the effectiveness of this approach, demonstrating its potential to Pareto-efficiently trade approximation quality against energy consumption.