Add JOSS 2.0 paper draft

.github/workflows/draft-pdf.yml

@@ -0,0 +1,19 @@
+on: [push]
+
+jobs:
+  paper:
+    runs-on: ubuntu-latest
+    name: Paper Draft
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v6
+      - name: Build draft PDF
+        uses: openjournals/openjournals-draft-action@master
+        with:
+          journal: joss
+          paper-path: paper/paper.md
+      - name: Upload
+        uses: actions/upload-artifact@v7
+        with:
+          name: paper
+          path: paper/paper.pdf

README.md

@@ -38,6 +38,10 @@ All are ultimately smoothing with similar runtime and accuracy, but some have fl
 
 All methods have hyperparameters, described in the [Sphinx documentation](https://pynumdiff.readthedocs.io/master/). We take a principled approach and propose a multi-objective optimization framework for choosing settings that minimize a loss function that balances faithfulness to data with smoothness of the derivative estimate. For more details, refer to [this paper](https://doi.org/10.1109/ACCESS.2020.3034077).
 
+![Three simulated signals and their derivatives, estimated by six of the seven method families, with hyperparameters chosen by `pynumdiff.optimize`.](paper/methods_comparison.png)
+
+Above, three simulated signals are differentiated by two methods each, drawn from six of the seven families, with hyperparameters chosen automatically by `pynumdiff.optimize`. Reproduce with `python paper/make_figure.py`.
+
 ## Installing
 
 Dependencies are listed in [pyproject.toml](https://github.com/florisvb/PyNumDiff/blob/master/pyproject.toml). They include the usual suspects like `numpy` and `scipy`, plus `pywavelets` for `waveletdiff`, `tqdm` for the optimizer, and `cvxpy` for `robustdiff` and `tvrdiff`.

paper/make_figure.py

@@ -0,0 +1,62 @@
+"""Generates paper/methods_comparison.png. Run from the repo root: python paper/make_figure.py"""
+import numpy as np, matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from pynumdiff.utils import simulate
+from pynumdiff import polydiff, tvrdiff, rtsdiff, spectraldiff, butterdiff, lineardiff
+from pynumdiff.optimize import optimize
+
+# One color per method, fixed wherever it appears. Okabe-Ito, legible to colorblind readers.
+STYLE = {spectraldiff:("spectraldiff","#CC79A7"), polydiff:("polydiff","#0072B2"), tvrdiff:("tvrdiff","#D55E00"),
+         butterdiff:("butterdiff","#5D3A9B"), rtsdiff:("rtsdiff","#009E73"), lineardiff:("lineardiff","#E69F00")}
+
+# Six of the seven families, paired so each panel contrasts two. Bandlimits are optimizer inputs, round numbers a
+# user reads off a power spectrum; Lorenz is the faster signal. Comment out FITTED to re-run the search (minutes).
+panels = [("Sum of sines", simulate.sine, [spectraldiff, polydiff], 1),
+          ("Triangle wave", simulate.triangle, [tvrdiff, butterdiff], 1),
+          ("Lorenz $x$", simulate.lorenz_x, [rtsdiff, lineardiff], 2)]
+FITTED = {"spectraldiff": dict(cutoff_freq=0.0625, even_extension=True, pad_to_zero_dxdt=True),
+          "polydiff": dict(stride=7, degree=2, window_size=41, kernel='gaussian'),
+          "tvrdiff": dict(gamma=10.6015625, huberM=6.0, order=1),
+          "butterdiff": dict(cutoff_freq=0.05, num_iterations=1, filter_order=2),
+          "rtsdiff": dict(log_qr_ratio=3.81328125, order=1, forwardbackward=False),
+          "lineardiff": dict(gamma=0.00011125, window_size=53, order=2, kernel='friedrichs')}
+#FITTED = {}
+
+def main():
+    fig, axes = plt.subplots(2, 3, figsize=(13, 5.4), sharex=True,
+                             gridspec_kw={'height_ratios':[1, 1.6], 'hspace':0.13, 'wspace':0.2})
+    for j, (sname, sim, methods, bandlimit) in enumerate(panels):
+        x, x_truth, dxdt_truth = sim(duration=4, dt=0.01, noise_parameters=(0, 0.2), random_seed=3)
+        t = np.arange(len(x))*0.01
+        top, bot = axes[0, j], axes[1, j]
+
+        top.plot(t, x, '.', color='0.72', markersize=1.6, label="noisy data")
+        top.plot(t, x_truth, '-', color='black', linewidth=1.1, label="true $x$")
+        top.set_title(sname, fontsize=11, pad=6)
+        bot.plot(t, dxdt_truth, '-', color='0.55', linewidth=2.6, label="true $\\dot{x}$", zorder=1)
+
+        for method in methods:
+            name, color = STYLE[method]
+            # Order 1 represents the triangle's piecewise-constant derivative exactly; without it tvrdiff goes spiky.
+            ssu = {'order':{1, 2, 3}} if (method is tvrdiff and sim is simulate.triangle) else {}
+            params = FITTED.get(name) or optimize(method, x, 0.01, bandlimit=bandlimit, search_space_updates=ssu)[0]
+            print(f"  {sname:<14} {name:<13} {params}", flush=True)
+            bot.plot(t, method(x, 0.01, **params)[1], '-', color=color, linewidth=1.1, label=name, zorder=2)
+        bot.set_xlabel("time (s)", fontsize=10)
+
+        for ax, pad in ((top, 0.17 if j == 0 else 0.04), (bot, 0.28)): # only the headroom each legend needs
+            lo, hi = ax.get_ylim(); ax.set_ylim(lo, hi + pad*(hi - lo))
+            ax.tick_params(labelsize=8)
+            for s in ('top', 'right'): ax.spines[s].set_visible(False)
+        bot.legend(fontsize=8, frameon=False, loc='upper center', ncol=3, handlelength=1.6, columnspacing=1.1,
+                   borderpad=0.1, title=f"optimized at bandlimit {bandlimit} Hz", title_fontsize=8)
+
+    axes[0, 0].set_ylabel("$x$", fontsize=11)
+    axes[1, 0].set_ylabel("$dx/dt$", fontsize=11)
+    axes[0, 0].legend(fontsize=8, frameon=False, loc='upper center', ncol=2, handlelength=1.6, borderpad=0.1)
+    fig.savefig("paper/methods_comparison.png", dpi=200, bbox_inches='tight')
+    print("wrote paper/methods_comparison.png")
+
+if __name__ == "__main__": # spawned workers re-import this module, so nothing heavy may run at import time
+    main()

paper/paper.bib

@@ -0,0 +1,181 @@
+@article{vanBreugel2022,
+  doi       = {10.21105/joss.04078},
+  url       = {https://doi.org/10.21105/joss.04078},
+  year      = {2022},
+  publisher = {The Open Journal},
+  volume    = {7},
+  number    = {71},
+  pages     = {4078},
+  author    = {{van Breugel}, Floris and Liu, Yuying and Brunton, Bingni W. and Kutz, J. Nathan},
+  title     = {{PyNumDiff}: A {Python} package for numerical differentiation of noisy time-series data},
+  journal   = {Journal of Open Source Software}
+}
+
+@misc{komarov2025,
+  title         = {A Taxonomy of Numerical Differentiation Methods},
+  author        = {Komarov, Pavel and {van Breugel}, Floris and Kutz, J. Nathan},
+  year          = {2025},
+  eprint        = {2512.09090},
+  archivePrefix = {arXiv},
+  primaryClass  = {math.NA},
+  url           = {https://arxiv.org/abs/2512.09090}
+}
+
+@article{vanBreugel2020numerical,
+  doi     = {10.1109/ACCESS.2020.3034077},
+  year    = {2020},
+  author  = {{van Breugel}, Floris and Kutz, J. Nathan and Brunton, Bingni W.},
+  journal = {IEEE Access},
+  title   = {Numerical differentiation of noisy data: A unifying multi-objective optimization framework},
+  volume  = {8},
+  pages   = {196865--196877}
+}
+
+@article{chartrand2011numerical,
+  author  = {Rick Chartrand},
+  title   = {Numerical differentiation of noisy, nonsmooth data},
+  journal = {ISRN Applied Mathematics},
+  year    = {2011},
+  volume  = {2011},
+  pages   = {164564},
+  doi     = {10.5402/2011/164564}
+}
+
+@article{brunton2016discovering,
+  author    = {Steven L. Brunton and Joshua L. Proctor and J. Nathan Kutz},
+  title     = {Discovering governing equations from data by sparse identification of nonlinear dynamical systems},
+  journal   = {Proceedings of the National Academy of Sciences},
+  year      = {2016},
+  volume    = {113},
+  number    = {15},
+  pages     = {3932--3937},
+  doi       = {10.1073/pnas.1517384113}
+}
+
+@article{virtanen2020scipy,
+  author  = {Pauli Virtanen and Ralf Gommers and Travis E. Oliphant and others},
+  title   = {{SciPy} 1.0: Fundamental algorithms for scientific computing in {Python}},
+  journal = {Nature Methods},
+  year    = {2020},
+  volume  = {17},
+  pages   = {261--272},
+  doi     = {10.1038/s41592-019-0686-2}
+}
+
+@article{harris2020array,
+  author  = {Charles R. Harris and K. Jarrod Millman and St{\'{e}}fan J. {van der Walt} and others},
+  title   = {Array programming with {NumPy}},
+  journal = {Nature},
+  year    = {2020},
+  volume  = {585},
+  pages   = {357--362},
+  doi     = {10.1038/s41586-020-2649-2}
+}
+
+@article{diamond2016cvxpy,
+  author  = {Steven Diamond and Stephen Boyd},
+  title   = {{CVXPY}: A {Python}-embedded modeling language for convex optimization},
+  journal = {Journal of Machine Learning Research},
+  year    = {2016},
+  volume  = {17},
+  number  = {83},
+  pages   = {1--5}
+}
+
+@article{savitzky1964,
+  author  = {Abraham Savitzky and Marcel J. E. Golay},
+  title   = {Smoothing and Differentiation of Data by Simplified Least Squares Procedures},
+  journal = {Analytical Chemistry},
+  year    = {1964},
+  volume  = {36},
+  number  = {8},
+  pages   = {1627--1639},
+  doi     = {10.1021/ac60214a047}
+}
+
+@article{huber1964,
+  author  = {Peter J. Huber},
+  title   = {Robust Estimation of a Location Parameter},
+  journal = {The Annals of Mathematical Statistics},
+  year    = {1964},
+  volume  = {35},
+  number  = {1},
+  pages   = {73--101},
+  doi     = {10.1214/aoms/1177703732}
+}
+
+@article{rauch1965,
+  author  = {Herbert E. Rauch and F. Tung and Charlotte T. Striebel},
+  title   = {Maximum likelihood estimates of linear dynamic systems},
+  journal = {AIAA Journal},
+  year    = {1965},
+  volume  = {3},
+  number  = {8},
+  pages   = {1445--1450},
+  doi     = {10.2514/3.3166}
+}
+
+@article{aravkin2013,
+  author  = {Aleksandr Y. Aravkin and James V. Burke and Gianluigi Pillonetto},
+  title   = {Optimization viewpoint on {Kalman} smoothing with applications to robust and sparse estimation},
+  journal = {Journal of Machine Learning Research},
+  year    = {2013},
+  volume  = {14},
+  pages   = {2513--2558},
+  url     = {https://jmlr.org/papers/volume14/aravkin13a/aravkin13a.pdf},
+  doi     = {10.1007/978-3-642-38398-4_8}
+}
+
+@software{derivative_pkg,
+  author    = {Andy Goldschmidt},
+  title     = {derivative: Numerical differentiation in {Python}},
+  year      = {2021},
+  url       = {https://github.com/andgoldschmidt/derivative}
+}
+
+@software{findiff,
+  author    = {Matthias Baer},
+  title     = {findiff: Finite difference derivatives in {Python}},
+  year      = {2018},
+  url       = {https://github.com/maroba/findiff}
+}
+
+@software{pykalman,
+  author    = {Daniel Duckworth and {The pykalman developers}},
+  title     = {pykalman: {Kalman} filters and smoothers for {Python}},
+  year      = {2012},
+  url       = {https://github.com/pykalman/pykalman}
+}
+
+@article{kalman1960,
+  author  = {Rudolf E. Kalman},
+  title   = {A new approach to linear filtering and prediction problems},
+  journal = {Journal of Basic Engineering},
+  year    = {1960},
+  volume  = {82},
+  number  = {1},
+  pages   = {35--45},
+  doi     = {10.1115/1.3662552}
+}
+
+@article{pysindy,
+  author  = {Brian M. de Silva and Kathleen Champion and Markus Quade and Jean-Christophe Loiseau and J. Nathan Kutz and Steven L. Brunton},
+  title   = {{PySINDy}: A {Python} package for the sparse identification of nonlinear dynamics from data},
+  journal = {Journal of Open Source Software},
+  year    = {2020},
+  volume  = {5},
+  number  = {49},
+  pages   = {2104},
+  doi     = {10.21105/joss.02104}
+}
+
+@article{lee2019pywavelets,
+  author  = {Gregory R. Lee and Ralf Gommers and Filip Wasilewski and Kai Wohlfahrt and Aaron O'Leary},
+  title   = {{PyWavelets}: A {Python} package for wavelet analysis},
+  journal = {Journal of Open Source Software},
+  year    = {2019},
+  volume  = {4},
+  number  = {36},
+  pages   = {1237},
+  doi     = {10.21105/joss.01237}
+}