# A kinetic-based regularization method for data science applications

arXiv: https://arxiv.org/abs/2503.04857 · HTML: https://mlsanity.com/paper/2503.04857/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 6 of 6)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Efficient Machine Learning for Big Data: A Review](https://mlsanity.com/paper/1503.05296/) (2015)
- [On the optimization of hyperparameters in Gaussian process regression with the help of low-order high-dimensional model representation](https://mlsanity.com/paper/2112.01374/) (2021)

## Built on by (most cited first, 1 of 1)

- [Kinetic-based regularization: Learning spatial derivatives and PDE applications](https://mlsanity.com/paper/2603.06380/) (2026)

## Abstract (arXiv)

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.