Pseudodynamics+

Physics Informed Neural Network based method for solving the single-cell population dynamics. For each cell, we estimate the dynamic parameter of the cell proliferation, differentiation and diffusion.

Documentation and tutorials

Full documentation, API reference, and step-by-step tutorials live on Read the Docs:

• Website: https://pseudodynamics-plus.readthedocs.io

• Tutorials (data preparation, config setup, downstream analysis): https://pseudodynamics-plus.readthedocs.io/en/latest/tutorials.html

• Config example: https://pseudodynamics-plus.readthedocs.io/en/latest/notebooks/setup_config.html

If you are getting started, read the tutorials first — they cover the input format and the most common pitfalls.

Installation

git clone https://github.com/Gottgens-lab/pseudodynamics_plus.git
cd pseudodynamics_plus
pip install -e .

Training

Store the population size information in AnnData.uns['pop'] and save as h5ad. Configure the training settings in config.json (see the config tutorial or any V0_config.json under logs/). Then run:

# with GPU
python main_train.py --config_path config.json -G 0

# without GPU
python main_train.py --config_path config.json -G None

Training options (diffusion_improvement features)

The diffusion_improvement branch adds several opt-in training features on top of the base PINN loss (log-density reconstruction + Fokker–Planck residual + Neural-ODE simulation). Every flag below defaults to the pre-2026-06 behaviour, so a run launched without any of them reproduces the original model. Pass a flag only to turn its feature on.

Growth loss

Flag	Default	Choices / type	What it does
--growth_loss_mode	legacy	legacy | logratio | massbalance	How the growth field g is constrained against observed population change. legacy (default, reproduces earlier runs): loss_fn(mass_gain, predicted_gain)/mass_gain with mass_gain = Σu_{t+1} − Σu_t, predicted_gain = Σg; absolute-scale and batch-size sensitive. Known caveat: dividing a non-negative loss by the signed mass_gain flips the gradient sign when the population shrinks. logratio (scale-free): constrains d ln N/dt = E_p[g], i.e. log(N_{t+1}/N_t) = ½(E_p[g_t]+E_p[g_{t+1}])·dt with density-weighted mean E_p[g] = (g·u).sum()/u.sum(); depends only on g averaged over cells, so g cannot hide behind a mis-scaled density net. massbalance: matches N_t + ∫∫ g·u dt to N_{t+1} in log space using the pop-scaled neural-ODE density.
--growth_pop_ref	cellsum	cellsum | popmean	Reference for the observed N_{t+1}/N_t ratio used by the growth loss. cellsum = batch cell-sum ratio (self-normalising); popmean = true population ratio carried in AnnData.uns['pop']/relmass (open-system anchor).
--g_init_rate	off (None)	float	Warm-start the growth net so g(x,t) ≈ this value at init (e.g. ln(N_{t+1}/N_t)/dt); prevents g collapsing to 0.

Fokker–Planck residual

Flag	Default	Choices / type	What it does
--residual_mode	raw	raw | ginv	FP residual formulation. raw = u²-scaled MSE (original). ginv = normalize the residual by u so it supervises g directly via the continuity inversion g = (∂u/∂t + ∇·(vu) − ∇·(D∇u))/u (scale-free; use a moderate --R_weight).
--R_weight	model default 1	float	Weight balancing the PDE residual loss against the data-fit loss.

Diffusion field D

Flag	Default	Choices / type	What it does
--D_penalty	model default 0.1	float	Weight (λ_D) of the L2 penalty on D; larger → smaller `
--D_var_weight	off (0)	float	Weight for the diffusion variance-matching + entropy losses (encourage D to track local expression variance / density-change entropy). 0 disables both.
--D_clip	off (None)	"lo,hi"	Hard-clamp the diffusion field into (lo, hi) wherever D enters the PDE dynamics (e.g. "-0.05,0.05").

Velocity / optimal transport (CFM)

Flag	Default	Choices / type	What it does
--cfm_weight	off (0)	float	Weight for the Conditional Flow Matching velocity loss (supervises v by OT-paired endpoints).
--cfm_unbalanced_reg_m	off (None = balanced)	float	If set, use unbalanced OT (marginal-relaxation reg_m) for the CFM pairing instead of balanced OT. Helps when population growth makes balanced coupling force spurious pairings.
--neuralode_weight	model default 2	float	Weight of the Neural-ODE density-simulation loss.
--deltax_weight	1e-2	float	Weight (λ_v) supervising v against the RNA-velocity-style deltax (set to 0 under the OT assumption).

Density estimation

Flag	Default	Choices / type	What it does
--density_estimator	kde	kde | gmm	Estimator for the observed density u_obs. kde = scipy.stats.gaussian_kde; gmm = sklearn GaussianMixture with BIC-selected components.
--gmm_k_max	5	int	Max number of GMM components tested by BIC when --density_estimator gmm.

Constructor-only knobs (not yet exposed on the CLI)

These are pde_params(...) arguments with no main_train.py flag; they take their class default unless the model is constructed directly. Listed here because they affect training and are not recorded in V0_config.json:

Argument	Default	Choices / type	What it does
d_penalty_mode	legacy	legacy | mean	legacy = ‖D‖₂.sum() (batch-size dependent); mean = D².mean() (batch-size invariant).
residual_mode='rcg'	—	—	Residual-Centered Growth: replaces the R-loss with a mean-corrected ginv target + a relmass magnitude anchor. The class accepts rcg even though --residual_mode only lists raw/ginv.
ema_decay, rcg_warmup_steps, rcg_clip_pct, rcg_u_net_raw_weight	0.95, 300, 0.02, 0.05	float/int	RCG hyperparameters; active only when residual_mode='rcg'. The EMA buffers (_Eg_resid_ema, _ema_initialized) are registered unconditionally, so checkpoints trained before this feature require strict=False to load.

Reproducibility note. Training flags above are not all persisted into logs/<exp>/V0_config.json (only the historical weight knobs are). To reproduce a run exactly, record the full command line, or pin the flags explicitly. For a clean ablation that varies only one parameter, fix every other flag to the same value across arms.

Branches

• main — stable release used by the docs and pip install.

• diffusion_improvement — active development branch with the latest improvements to the diffusion term, new training scripts, and ongoing experiments. Check this branch if you want the most recent features or want to reproduce results from the current manuscript revision.

git checkout diffusion_improvement

Updates

Reverse-chronological log of the latest functionality on diffusion_improvement.

2026-06-16 — main_train_rcg.py: clean RCG training entry point

A dedicated training script for the RCG (Residual-Centered Growth) PINN, kept separate from main_train.py so RCG runs launch without the original script’s config-override foot-guns:

• --config is merged with CLI args — unspecified CLI flags no longer clobber config values.

• Exposes every RCG flag and ships defaults that match the recommended launch config (--residual_mode defaults to rcg, --growth_loss_mode to logratio).

• Runs the CFM loop once (cfm_loops=1) and uses the batch-size-invariant diffusion penalty (d_penalty_mode='mean', i.e. D.pow(2).mean()).

• --gpu_devices defaults to "0".

python main_train_rcg.py --dataset <h5ad_stem> --config logs/<exp>/V0_config.json

The RCG residual mode itself (residual_mode='rcg' — mean-corrected ginv target plus a relmass magnitude anchor) is documented in the Constructor-only knobs table above.

Reproducible configs and checkpoints

The logs/ directory contains the exact configs and trained checkpoints for every experiment in the manuscript and rebuttals (Klein, Tom, cord blood, synthetic Fokker–Planck, ablations, etc.). Each experiment directory follows the same layout:

logs/<experiment_name>/
├── V0_config.json         # training config used to reproduce the run
└── lightning_logs/        # PyTorch Lightning checkpoints and metrics

To reproduce a run, point main_train.py at the stored config:

python main_train.py --config_path logs/<experiment_name>/V0_config.json -G 0

Important resources

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Tutorials

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Tutorials