BINO-SD

Official source code for the ICANN 2026 paper:

Beyond Smooth Darcy: Evaluation Changes the Conclusion in Sparse-Sensor Inverse Learning

This repository contains the reproducible experiment code for the paper, including Darcy benchmark generation, sparse-sensor inverse learning, evaluation scripts, and paper-table utilities.

This project is a minimal landing implementation for the first item in PDE.txt:

inverse problem + experimental design + Bayesian neural operator

The code instantiates a small but complete pipeline:

• generate a synthetic Darcy / diffusion inverse dataset locally;
• scale to larger and more realistic benchmark families;
• learn a differentiable sparse sensor layout;
• infer a posterior mean and log-variance for the hidden coefficient field;
• regularize the inverse model with a PDE residual term.

• scripts/generate_dataset.py: builds a synthetic Darcy inverse dataset.
• scripts/generate_benchmark_suite.py: generates larger benchmark-suite datasets.
• scripts/run_benchmark_preset.py: launches named large-benchmark train/eval presets.
• scripts/train.py: trains the Bayesian inverse operator.
• scripts/evaluate.py: evaluates a checkpoint and writes plots and metrics.
• scripts/aggregate_results.py: aggregates multiple runs into markdown and JSON summaries.
• scripts/make_paper_tables.py: generates paper-style markdown and LaTeX tables.
• scripts/make_method_figure.py: draws a method overview figure for reports or drafts.
• scripts/make_dataset_figure.py: renders representative coefficient/solution/forcing examples from a dataset.
• scripts/setup_env.ps1: creates the conda environment and installs dependencies.
• src/bi_operator/pde.py: PDE sampler, solver, and physics residual.
• src/bi_operator/model.py: soft sensor layer and FNO-style inverse model.
• src/bi_operator/data.py: dataset loading helpers.

cd <repo>
powershell -ExecutionPolicy Bypass -File .\scripts\setup_env.ps1

conda run -n pde_inverse_operator python .\scripts\generate_dataset.py --output .\data\darcy_inverse_dataset.npz
conda run -n pde_inverse_operator python .\scripts\train.py --dataset .\data\darcy_inverse_dataset.npz --output-dir .\artifacts\baseline_run
conda run -n pde_inverse_operator python .\scripts\evaluate.py --dataset .\data\darcy_inverse_dataset.npz --checkpoint .\artifacts\baseline_run\best_model.pth --output-dir .\artifacts\baseline_run

If you want to use the RTX 5090 on this machine, a separate GPU environment is available:

cd <repo>
powershell -ExecutionPolicy Bypass -File .\scripts\setup_gpu_env.ps1

This creates pde_inverse_operator_gpu and installs a CUDA 12.8 PyTorch build without disturbing the CPU environment.

• The dataset is generated locally, so there is no external download dependency.
• The model predicts a Gaussian posterior over the log-coefficient field.
• Sensor design is differentiable: the sensor maps are trainable and sharpened via entropy and diversity regularization.
• The current implementation is a research prototype meant to be runnable end to end, not a final large-scale benchmark.
• The newer darcy_structured_realistic benchmark family adds signed multisource forcing, nonzero Dirichlet boundaries, and optional noisy interior observations.
• Large generated datasets, checkpoints, plots, and run artifacts are intentionally excluded from Git. They can be regenerated with the scripts above, or restored locally under data/ and artifacts/.

• Current paper-track best single run on the main 20x20 constant-forcing task: artifacts/abl_sensors24 test NLL about -0.4921 test RMSE about 0.4632
• Current paper-track best stable 20x20 constant-forcing result: artifacts/multiseed_summary_24s.md RMSE mean about 0.4641, std about 0.0027 NLL mean about -0.4904, std about 0.0080
• Current paper-track best 32x32 constant-forcing run: artifacts/task_constant32_lgr test NLL about -0.5907 test RMSE about 0.4322
• Current best learned-sensor hard-task 32x32 multisource-forcing run: artifacts/task_multisource32_big40 test NLL about -0.3363 test RMSE about 0.5164
• Current best matched-budget random-grid hard-task run: artifacts/task_multisource32_random40 test NLL about -0.3849 test RMSE about 0.5041
• Current hard-task matched-40 layout summary: artifacts/multisource32_layout_matched40_summary.md
• Current hard-task random40 multi-seed summary: artifacts/multiseed_summary_multisource32_random40.md RMSE mean about 0.5247, std about 0.0175 NLL mean about -0.3286, std about 0.0514
• Current larger structured benchmark run: artifacts/task_structured48_big40_v2 test NLL about -0.1185 test RMSE about 0.6704
• Current realistic scale-up dataset: data/darcy_structured_realistic_64_medium.npz 64x64, 1024/160/160, interior observation noise 0.03
• Current realistic 64x64 best single run: artifacts/task_structured_realistic64_main64s test NLL about 1.2622 test RMSE about 1.2250
• Current realistic 64x64 multi-seed summary: artifacts/multiseed_summary_realistic64_64s.md RMSE mean about 1.2251, std about 0.0005
• Current realistic 80x80 scale-up run: artifacts/task_structured_realistic80_main test NLL about 1.4239 test RMSE about 1.2633
• Current realistic 80x80 multi-seed summary: artifacts/multiseed_summary_realistic80_56s.md RMSE mean about 1.2647, std about 0.0012
• Current realistic 96x96 first run: artifacts/task_structured_realistic96_main test NLL about 1.6389 test RMSE about 1.2970
• Current realistic 96x96 multi-seed summary: artifacts/multiseed_summary_realistic96_72s.md RMSE mean about 1.2962, std about 0.0006
• Current realistic 96x96 baseline summary: artifacts/realistic96_baseline_summary.md
• Main-task large dataset file: data/darcy_inverse_dataset_large.npz
• Structured larger-scale dataset file: data/darcy_structured_multisource_48_large.npz
• Realistic benchmark scale-up summary: artifacts/benchmark_realism_scale_update_2026-03-22.md
• Benchmark suite manifest: artifacts/benchmark_suite_conference_scale.md

• Baseline comparison: artifacts/baseline_summary.md
• Ablation study: artifacts/ablation_summary.md
• Multi-seed summary for the 16-sensor main config: artifacts/multiseed_summary.md
• Multi-seed summary for the 24-sensor main config: artifacts/multiseed_summary_24s.md
• Multi-seed summary for the 32x32 multisource big-40 config: artifacts/multiseed_summary_multisource32_big40.md
• Matched 40-sensor layout comparison on the 32x32 multisource task: artifacts/multisource32_layout_matched40_summary.md
• Multi-seed summary for the 32x32 multisource random-40 config: artifacts/multiseed_summary_multisource32_random40.md
• Task and scale summary: artifacts/taskscale_summary.md
• Multisource 32x32 tuning summary: artifacts/multisource_tuning_summary.md
• Structured 48x48 baseline summary: artifacts/structured48_baseline_summary.md
• Realistic 64x64 baseline summary: artifacts/realistic64_baseline_summary.md
• Realistic 64x64 multi-seed summary: artifacts/multiseed_summary_realistic64_64s.md
• Realistic 80x80 baseline summary: artifacts/realistic80_baseline_summary.md
• Realistic 80x80 multi-seed summary: artifacts/multiseed_summary_realistic80_56s.md
• Realistic 96x96 baseline summary: artifacts/realistic96_baseline_summary.md
• Realistic 96x96 multi-seed summary: artifacts/multiseed_summary_realistic96_72s.md
• Paper-style markdown / LaTeX tables: artifacts/paper_tables_2026-03-22.md artifacts/paper_tables_2026-03-22.tex
• Method overview figure: artifacts/method_overview.png
• Structured 48x48 dataset example: artifacts/structured48_dataset_example.png
• Paper positioning memo: artifacts/PAPER_POSITIONING_2026-03-22.md

Current key takeaways:

• On the main large 20x20 constant-forcing task, the best trainable sensor design remains learned_gaussian_random, and increasing the sensor count from 16 to 24 improves the single-run RMSE from about 0.4684 to about 0.4632.
• The 24-sensor main-task result is now backed by a three-seed summary: RMSE mean about 0.4641, std about 0.0027
• The previous weakest setting, the 32x32 multisource-forcing task, is now materially better: RMSE improves from about 0.5859 to about 0.5164 when moving to a larger learned sensor budget and a stronger operator backbone.
• The new matched-budget 40-sensor controls show that the hard task is also much more layout-sensitive than the smooth main task: random40 reaches about 0.5041 RMSE in the reference seed, while fixed40 reaches about 0.5290.
• The corresponding hard-task three-seed summaries are now close enough to change the paper story: learned40 is about 0.5285 +/- 0.0107 RMSE, while random40 is about 0.5247 +/- 0.0175.
• This makes the current strongest paper angle benchmark-centered rather than method-centered: the hard benchmark exposes layout sensitivity and ranking instability, while the realistic scale-up line exposes calibration degradation.
• The project now also includes a larger 48x48 structured multisource benchmark to move beyond purely smooth Fourier-style coefficient fields.
• The project now also includes a 64x64 structured realistic benchmark with signed forcing, nonzero boundaries, and noisy observations to increase conference-style workload and realism.
• On the new 64x64 structured realistic benchmark, the best Bayesian learned-sensor configuration uses 64 sensors and reaches about 1.2251 +/- 0.0005 RMSE over three seeds.
• A first 80x80 structured realistic run is now available, so the project has moved beyond a single scale-up point at 64x64.
• The 80x80 structured realistic benchmark now also has baseline comparisons and a three-seed summary, which makes the realistic scale-up line much more substantial.
• The 96x96 structured realistic benchmark now also has random-grid and fixed-grid Bayesian baselines, plus a three-seed summary, so it is no longer only a scale-showing point.
• The current 96x96 three-seed summary is about 1.2962 +/- 0.0006 RMSE, while the deterministic operator remains slightly best in pure RMSE at about 1.2959.
• On that 48x48 structured benchmark, the current Bayesian learned-sensor model is slightly better than both the random_grid Bayesian baseline and the deterministic operator baseline.

• The stable main line is still the learned Gaussian-random sensor design without forcing-sensor fusion.
• An exploratory branch is now implemented via: --use-forcing-sensor-fusion This is meant for future work on harder multisource settings, but the first run was not yet better than the current non-fusion best model.