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This repo provides the official implementation of the NeurIPS2024 paper Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators.

Installation

Simply run

pip install .

How to run the minimal example script

For reader who do not wish to go through the entire repo, the script sine_gordon.py provides a minimal implementation of the sine-gordon equation described in Appendix I.1. The default hyperparmeter setting follows the description in Appendix H. To run sparse STDE for 100kD Sine-Gordon with randomization batch of 16:

python sine_gordon.py --sparse --dim 100000 --rand_batch_size 16

How to reproduce results shown in the paper

Inseparable and effectively high-dimensional PDEs

To run the 100kD two-body Allen-Cahn equation described in Appendix I.1. with sparse STDE:

./scripts/insep.sh --config.eqn_cfg.rand_batch_size 16 --config.eqn_cfg.hess_diag_method sparse_stde --config.eqn_cfg.dim 100000 --config.eqn_cfg.name AllenCahnTwobody

To run other equations, change the flag --config.eqn_cfg.name. See the list of equation name in stde/config.py.

To get memory usage, add the following flags --get_mem --n_runs 1 --config.test_cfg.n_points 200, which runs a few epochs to determine the peak GPU memory usage.

You will find the experiment summary and saved checkpoints in the _results folder.

Semilinear Parabolic PDEs

To run the 10kD Semilinear Heat equation described in Appendix I.2. with sparse STDE:

./scripts/semilinear_parabolic.sh --config.eqn_cfg.name SemilinearHeatTime --config.eqn_cfg.dim 10000 --config.eqn_cfg.hess_diag_method sparse_stde --config.eqn_cfg.rand_batch_size 16

Weight sharing

To enable weight sharing described in Appendix G and I.3, add the --config.model_cfg.block_size flag. For example:

./scripts/insep.sh --config.eqn_cfg.rand_batch_size 16 --config.eqn_cfg.hess_diag_method sparse_stde --config.eqn_cfg.dim 100000 --config.eqn_cfg.name AllenCahnTwobody --config.model_cfg.block_size 50

High-order PDEs

To run the high-order low-dimensional PDEs described in Appendix I.4.1, change the '--config.eqn_cfg.name' flag accordingly. For example, to run the Gradient-enhanced 1D Korteweg-de Vries (g-KdV) equation:

./scripts/insep.sh --config.eqn_cfg.rand_batch_size 0 --config.eqn_cfg.hess_diag_method sparse_stde --config.eqn_cfg.dim 1 --config.eqn_cfg.name highord1d

To run the amortized gradient-enhanced PINN described in Appendix I.4.2, change the '--config.eqn_cfg.name' flag accordingly. For example, to run two-body Allen-Cahn equation with amoritzed gPINN:

./scripts/insep.sh --config.eqn_cfg.rand_batch_size 16 --config.eqn_cfg.hess_diag_method sparse_stde --config.eqn_cfg.dim 100000 --config.eqn_cfg.name AllenCahnTwobodyG --config.eqn_cfg.gpinn_weight 0.1