updated ReadMe

README.md

@@ -1,36 +1,183 @@
-# SynPAT: Synthetic Physical Theories with Data
+# SynPAT: Generating Synthetic Physical Theories with Data
 
-This dataset contains systems of dimensionally consistent equations generated across various configurations of:
+This is the Hugging Face dataset entry for **SynPAT**, a synthetic theory and data generation system developed for the paper:  
+**SynPAT: Generating Synthetic Physical Theories with Data**  
+GitHub: [https://github.com/jlenchner/theorizer](https://github.com/jlenchner/theorizer)
 
-- Number of variables: 6 to 9
-- Number of derivatives: 2 to 4
-- Number of equations: 4 to 6
+SynPAT generates symbolic physical systems and corresponding synthetic data to benchmark symbolic regression and scientific discovery algorithms. Each synthetic system includes symbolic equations, dimensionally consistent variables/constants, algebraic consequences, and both clean and noisy datasets.
 
-Each configuration includes three generated systems with:
+---
 
-- Symbolic equations (`system.txt`)
-- Numerical data (`system.dat`)
-- Replacements (`replacement_*.txt`)
-- Consequences (`consequence.txt`, `consequence.dat`)
-- Noisy variants for each noise level (`*_0.001.dat`, ..., `*_0.1.dat`)
+## Dataset Structure
 
-## Purpose
+The dataset is organized hierarchically by configuration and system index:
 
-Designed to benchmark symbolic regression models on machine-assisted physical discovery tasks.
+```
+dataset/{config}/System_{n}/
+```
 
-## File structure
 
-The dataset is packaged as a single `dataset.zip` archive. Inside are directories for each configuration (`vars_X_derivs_Y_eqns_Z/`) containing 3 systems each.
+Where:
+- `{v}` ∈ {6, 7, 8, 9} is the number of symbolic variables
+- `{d}` ∈ {2, 3, 4} is the number of derivatives (among the symbolic variables)
+- `{e}` ∈ {4, 5, 6} is the number of equations in the system
+- `{n}` ∈ {1, 2, 3} indexes the individual system instances per configuration
 
-## Citation
+Each `System_{n}` directory contains exactly 18 files:
 
-> Srivastava et al., **SynPAT: A System for Generating Synthetic Physical Theories with Data**, NeurIPS 2025 (submitted)
+### Symbolic System and Consequence:
+- `system.txt` — base symbolic system with metadata including variable types, units, constants, and equations
+- `consequence.txt` — derived consequence equation (single polynomial) with associated metadata
+
+### Clean Data:
+- `system.dat` — clean numerical dataset corresponding to `system.txt`
+- `consequence.dat` — clean data for the consequence polynomial
+
+### Noisy Data:
+For each noise level ε ∈ {0.001, 0.01, 0.05, 0.1}, the following files are included:
+- `system_ε.dat` — noisy system data with Gaussian noise of standard deviation ε
+- `consequence_ε.dat` — noisy consequence data with Gaussian noise of standard deviation ε
+
+This results in:
+- 4 `system_ε.dat` files
+- 4 `consequence_ε.dat` files
+
+### Replacement Systems:
+- `replacement_1.txt` through `replacement_5.txt` — versions of `system.txt` where one axiom has been replaced, used for consequence prediction benchmarking under ablation.
+
+### Summary of File Count per System:
+- 2 base files: `system.txt`, `consequence.txt`
+- 2 clean data files: `system.dat`, `consequence.dat`
+- 8 noisy data files: `system_ε.dat`, `consequence_ε.dat` for 4 ε values
+- 5 replacement files: `replacement_1.txt` through `replacement_5.txt`
+
+**Total per system:** 2 + 2 + 8 + 5 = **17 files**
+
+Each configuration folder (`vars_{v}_derivs_{d}_eqns_{e}`) contains exactly three systems: `System_1`, `System_2`, `System_3`.
+
+The full dataset spans all 4 × 3 × 3 = **36 configurations**, totaling **108 systems** and **1836 files**.
+
+
+## File Format Example
+
+### system.txt 
+
+`system.txt` contains the symbolic system, including variables, constants, derivatives, equations, and units:
+
+```text
+Variables: ['Fc', 'Fg', 'W', 'd1', 'd2', 'm1']  
+Constants: ['G', 'c']  
+Derivatives: ['dx1dt', 'd2x1dt2', 'dx2dt']  
+Equations:  
+dx1dt*dx2dt*d2*m1 - W*d1  
+d2x1dt2*W*m1 - Fc*Fg*d1  
+2*c*Fg + dx2dt*Fc - dx2dt*Fg  
+G*d2x1dt2*d2*m1 + G*Fc*d2 - G*W + 4*d2x1dt2*dx1dt^2*d1^2  
+-d2x1dt2*Fc*m1 + d2x1dt2*Fg*m1 + Fc*Fg  
+Units of Measure of Variables: ['s^(-2)*kg*m', 's^(-2)*kg*m', 'm^2*s^(-2)*kg', 'm', 'm', 'kg']  
+Units of Measure of Constants: ['1/kg*m^3*s^(-2)', '1/s*m']  
+Units of Measure of Derivatives: ['1/s*m', 's^(-2)*m', '1/s*m']  
+Units of Measure of Equations:  
+m^3*s^(-2)*kg  
+kg^2*m^3*s^(-4)  
+m^2*s^(-3)*kg  
+m^5*s^(-4)  
+kg^2*m^2*s^(-4)
+```
+
+### consequence.txt 
+
+`consequence.txt` includes **additional metadata** for data generation and symbolic regression tasks:
+
+```text
+Variables: ['Fc', 'Fg', 'W', 'd1', 'd2', 'm1']  
+Constants: ['G', 'c']  
+Derivatives: ['dx1dt', 'd2x1dt2', 'dx2dt']  
+Equations:  
+dx1dt*dx2dt*d2*m1 - W*d1  
+d2x1dt2*W*m1 - Fc*Fg*d1  
+2*c*Fg + dx2dt*Fc - dx2dt*Fg  
+G*d2x1dt2*d2*m1 + G*Fc*d2 - G*W + 4*d2x1dt2*dx1dt^2*d1^2  
+-d2x1dt2*Fc*m1 + d2x1dt2*Fg*m1 + Fc*Fg  
+Units of Measure of Variables: ['s^(-2)*kg*m', 's^(-2)*kg*m', 'm^2*s^(-2)*kg', 'm', 'm', 'kg']  
+Units of Measure of Constants: ['1/kg*m^3*s^(-2)', '1/s*m']  
+Units of Measure of Derivatives: ['1/s*m', 's^(-2)*m', '1/s*m']  
+Units of Measure of Equations:  
+m^3*s^(-2)*kg  
+kg^2*m^3*s^(-4)  
+m^2*s^(-3)*kg  
+m^5*s^(-4)  
+kg^2*m^2*s^(-4)
+
+Measured Variables: ['d1', 'Fg', 'm1', 'W']  
+Observed Constants: []  
+Measured Derivatives: ['d2x1dt2']  
+
+Target Polynomial:  
+d1*m1*d2x1dt2*Fg^2 - m1^2*d2x1dt2^2*W + m1*d2x1dt2*W*Fg
+```
+
+### replacement_i.txt
+
+`replacement_i.txt` has the same format as `system.txt` but with one axiom replaced by a different, dimensionally consistent axiom
+```text
+Variables: ['Fc', 'Fg', 'W', 'd1', 'd2', 'm1']
+Constants: ['G', 'c']
+Derivatives: ['dx1dt', 'd2x1dt2', 'dx2dt']
+Equations:
+dx1dt*dx2dt*d2*m1 - W*d1
+>>> c*Fc*d2 + c*Fg*d1 - dx1dt*Fg*d1 + dx2dt*Fg*d2 + dx2dt*W   <<< 
+2*c*Fg + dx2dt*Fc - dx2dt*Fg
+G*d2x1dt2*d2*m1 + G*Fc*d2 - G*W + 4*d2x1dt2*dx1dt^2*d1^2
+-d2x1dt2*Fc*m1 + d2x1dt2*Fg*m1 + Fc*Fg
+Units of Measure of Variables: ['s^(-2)*kg*m', 's^(-2)*kg*m', 'm^2*s^(-2)*kg', 'm', 'm', 'kg']
+Units of Measure of Constants: ['1/kg*m^3*s^(-2)', '1/s*m']
+Units of Measure of Derivatives: ['1/s*m', 's^(-2)*m', '1/s*m']
+Units of Measure of Equations:
+m^3*s^(-2)*kg
+m^3*s^(-3)*kg
+m^2*s^(-3)*kg
+m^5*s^(-4)
+kg^2*m^2*s^(-4)
+```
+
+### Data Files
+
+Each `.dat` file contains rows of numerical data corresponding to samples used for learning or evaluation. Each row represents one data point.
+
+**system_0.1.dat** (first few rows of noisy system data):
+
+```text
+1.925664644193098241e+00 2.872700594236812677e+00 ...
+```
+
+**Header of .dat files**:
+
+```text
+G c dx1dt d2x1dt2 dx2dt Fc W d1 Fg m1 d2
+1.000000 1.0000000 ......
+```
+
+- `system.dat` and its noisy versions (`system_0.001.dat`, `system_0.01.dat`, `system_0.05.dat`, `system_0.1.dat`) contain all variables, constants, and derivatives used in the full symbolic system. The data columns follow the same fixed order shown in the header.
+
+- `consequence.dat` and its noisy versions (`consequence_0.001.dat`, `consequence_0.01.dat`, etc.) contain only the subset of constants, derivatives, and variables needed to evaluate the consequence polynomial in `consequence.txt`. The columns are ordered as: constants first, followed by any measured derivatives, and then the measured variables.
+
+---
+
+## Authors
+
+- **Karan Srivastava** — University of Wisconsin-Madison (ksrivastava4@wisc.edu)  
+- **Jonathan Lenchner** — IBM T.J. Watson Research Center (lenchner@us.ibm.com)  
+- **Joao Goncalves** — IBM T.J. Watson Research Center (jpgoncal@us.ibm.com)  
+- **Lior Horesh** — IBM T.J. Watson Research Center (lhoresh@us.ibm.com)  
+
+---
 
 ## License
 
-[CC BY 4.0](https://creativecommons.org/licenses/by/4.0/)
+MIT License
 
-## Related resources
+---
 
-- 📘 [Project GitHub](https://github.com/jlenchner/theorizer)
-- 📄 [Croissant metadata](https://w3id.org/croissant)
+For issues, questions, or contributions, please visit:  
+[https://github.com/jlenchner/theorizer](https://github.com/jlenchner/theorizer)