# Synthics: Synthetic Physics-like Datasets for Machine Learning

arXiv: https://arxiv.org/abs/2606.06724 · HTML: https://mlsanity.com/paper/2606.06724/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Training Deep Networks with Synthetic Data: Bridging the Reality Gap by Domain Randomization](https://mlsanity.com/paper/1804.06516/) (2018)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Mitra: Mixed Synthetic Priors for Enhancing Tabular Foundation Models](https://mlsanity.com/paper/2510.21204/) (2025)
- [Probabilistic Grammars for Equation Discovery](https://mlsanity.com/paper/2012.00428/) (2020)
- [Efficient Generator of Mathematical Expressions for Symbolic Regression](https://mlsanity.com/paper/2302.09893/) (2023)
- [Chance-constrained Flow Matching for High-Fidelity Constraint-aware Generation](https://mlsanity.com/paper/2509.25157/) (2025)
- [Active Expansion Sampling for Learning Feasible Domains in an Unbounded Input Space](https://mlsanity.com/paper/1708.07888/) (2017)
- [Can Test-time Computation Mitigate Reproduction Bias in Neural Symbolic Regression?](https://mlsanity.com/paper/2505.22081/) (2025)

## Abstract (arXiv)

Representative data is fundamental in machine learning, as limited data hinders generalisation. Collecting sufficient real-world samples is often infeasible. Synthetic data generation offers a practical solution, but only if the generated data faithfully reflects the structure of real observations. In this paper, a method for generating synthetic regression datasets that structurally resemble physics equations from a given equation corpus is presented. The approach uses a Bayesian Probabilistic Context-Free Grammar to capture the underlying algebraic structure of the corpus, from which novel equations are sampled. To ensure the generated inputs lie within a physically meaningful domain, the applicability domain is characterised for each equation through non-intrusive probing, also recovering inter-variable constraints. Input sampling further mimics realistic experimental conditions by drawing from random sub-ranges of the valid domain with mixed uniform and truncated normal distributions. The generated data is statistically validated against the Feynman equation corpus using Kolmogorov-Smirnov tests. The generated equations match the corpus on all of the eight studied structural features, compared to only two for an unsmoothed purely probabilistic grammar, demonstrating that the Bayesian prior is essential for structural fidelity given the size of the corpus. In a downstream hyperparameter-tuning task, a gradient-boosted regressor tuned on the synthetic data picks, on average, the 6th-best configuration out of 20 on real data, matching the result of tuning on real data itself and substantially outperforming random expression trees (10th) and noise (19th).