SLIC

Code and data for

M. C. Chung, A. Zacharia and J. Guan, A sample-size-invariant scoring criterion for sparse model discovery, Communications Physics (under review).

Archived at Zenodo: doi:10.5281/zenodo.23001594. This DOI always resolves to the newest release.

SLIC (the sample-length-scaling information-like criterion) scores candidate models in sparse model discovery with a complexity penalty that grows in proportion to sample size, so that the balance between accuracy and sparsity does not shift as data accumulate.

Repository layout

Path	Contents
src/	SLIC implementation and supporting routines, including the effective sample size (neff.jl), WAIC and gMDL (waic_gmdl.jl), the no-projection pipeline (no_projection.jl) and exhaustive enumeration (enumeration.jl)
scripts/	Julia scripts for data generation, model discovery and the sloshing-tank experiment (sloshtank.jl)
scripts/analysis/	Julia scripts that compute the results in data/results/; common.jl holds the shared setup
scripts/figures_python/	Python scripts that draw the figures, with requirements.txt
data/exp_raw/	Experimental sloshing-tank data (Bauerlein and Avila, J. Fluid Mech. 2021)
data/results/	Analysis results behind each figure, one folder per figure (.jld, readable with HDF5)
data/source_data/	Source data for the main-text figures (Supplementary Data 1-4, Excel)

The results behind the figures are in data/results/. The folders data/sims/ode_results_main/ and data/sims/ode_results_si/ hold results from earlier runs of the benchmarks and are kept for reference. Files for other analyses from earlier stages of the project (partial differential equations, RNA-nanoparticle and kernel analyses) are retained but are not used in this paper.

Results and scripts for each figure

Figure	Computed by (scripts/analysis/)	Results in data/results/	Drawn by (scripts/figures_python/)
Fig. 1b, Supp. Fig. S1	fig1b_pool.py (Python)	fig1b_figS1/ (computed by fig1b_pool.py)	gen_fig1b_panel.py, gen_s1.py
Fig. 2, Supp. Fig. S2	fig2_benchmarks.jl	fig2_benchmarks/	gen_fig2_grid.py (Fig. 2 metrics grid), gen_s2.py (Supp. Fig. S2)
Fig. 3, Supp. Figs. S5-S8	fig3_perturbations.jl	fig3_perturbations/	gen_fig3_panels.py (Fig. 3 panels; run with dts, Ts, ss or ps), gen_s5_s8.py
Fig. 4, Supp. Fig. S13	scripts/sloshtank.jl	data/exp_raw/	scripts/sloshtank.jl; fig4_port.py reproduces the Fig. 4 predictions in Python
Supp. Figs. S3-S4	waic_gmdl_benchmarks.jl	figS3_S4_waic_gmdl/	gen_s3_s4.py
Supp. Fig. S9	no_projection_benchmarks.jl	figS9_no_projection/	gen_s9.py
Supp. Fig. S10	long_trajectory.jl	figS10_long_trajectory/	gen_s10.py
Supp. Fig. S11	duffing_sweep.jl	figS11_duffing/	gen_si_duffing.py
Supp. Fig. S12	enumerate_all.jl, after calibrate_c.jl (see Running the analysis scripts)	figS12_enumeration/	gen_s12.py
Supp. Table S1	probe_neff_definitions.jl	tableS1_neff_definitions/ (job logs; cases 1-4)

The Julia scripts write their results to data/sims/ode_results/; the copies used for the figures are in data/results/. The Python figure scripts read them directly and write to plots/; for example, from the repository root:

pip install -r scripts/figures_python/requirements.txt
python scripts/figures_python/fig1b_pool.py        # recomputes the Fig. 1b / Supp. Fig. S1 data (about 15 s)
python scripts/figures_python/gen_fig1b_panel.py

mlib.py holds the metric functions shared by several scripts, paperstyle.py the shared plotting style, and tickcheck.py checks that every axis's ticks enclose its plotted data. gen_s5_s8.py takes several minutes the first time, while it computes and caches the metrics.

Running the Julia code

This code base uses the Julia Language (version 1.10) and DrWatson. To reproduce the project locally:

1. Download this code base.
2. Open a Julia console and do:

   julia> using Pkg
   julia> Pkg.add("DrWatson") # install globally, for using `quickactivate`
   julia> Pkg.activate("path/to/this/project")
   julia> Pkg.instantiate()
   

This installs the package versions recorded in Project.toml and Manifest.toml. Most scripts start with

using DrWatson
@quickactivate "SLIC"

which activates the project and handles local paths.

Running the analysis scripts

Each script in scripts/analysis/ computes one task of a sweep. The task is chosen by the environment variable SLURM_ARRAY_TASK_ID, so a whole sweep can be submitted as a Slurm array job (for example sbatch --array=0-35), and a single task can be run locally from the repository root:

SLURM_ARRAY_TASK_ID=0 julia --project=. scripts/analysis/fig2_benchmarks.jl

Systems are numbered 1-6 (Lorenz, Rössler, Lotka-Volterra, Brusselator, Van der Pol, nonlinear pendulum) and noise levels 1-6 (0, 5, 10, 20, 30, 40 %). Where a task combines the two, task = 6 × (system - 1) + (noise level - 1).

Script	Tasks	Each task is	Other settings
fig2_benchmarks.jl	0-35	a system and noise level
fig3_perturbations.jl	0-35 (0-23 for ps)	a system and noise level	SLIC_SI_COND: dts (panel a), Ts (b), ss (c) or ps (d)
waic_gmdl_benchmarks.jl	0-35	a system and noise level
no_projection_benchmarks.jl	0-5	a system (all noise levels)
long_trajectory.jl	0-35	a system and trajectory-length factor L = 1, 2, 5, 10, 20, 50 (task = 6 × (system - 1) + L index)
duffing_sweep.jl	0-8	a value of alpha (0, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2)
probe_neff_definitions.jl	0-5	a case (0-3 give Supp. Table S1; 4-5 are the dt/5 oversampling test)
calibrate_c.jl, calibrate_gamma.jl			SLIC_CAL_SYS = 1-6, one run per system
enumerate_all.jl	0-11 (0-5 for the pendulum)	a noise level and equation, task = (number of equations) × (noise level - 1) + (equation - 1)	SLIC_ENUM_SYS = 3-6 and SLIC_GAMMA=100; run calibrate_c.jl for that system first

The larger sweeps were run on a cluster with 8 cores and 32-48 GB of memory per task (16 cores and 128 GB for long_trajectory.jl), with up to a day per task (three days for long_trajectory.jl).