Open Software for Astrophysics, AAS241

Slides for my plenary talk at the 241st American Astronomical Society meeting.

Transcript

1. OPEN SOFTWARE FOR ASTROPHYSICS Dan Foreman-Mackey
3. case study: Gaussian Processes
4. AAS 225 / 2015 / Seattle AAS 231 / 2018 / National Harbor
5. °0.6 °0.3 0.0 0.3 0.6 raw [ppt] 0 5 10 15 20 25 time [days] °0.30 °0.15 0.00 de-trended [ppt] N = 1000 reference: DFM+ (2017)
6. °0.6 °0.3 0.0 0.3 0.6 raw [ppt] 0 5 10 15 20 25 time [days] °0.30 °0.15 0.00 de-trended [ppt] N = 1000 reference: DFM+ (2017)
7. reference: Aigrain & DFM (2022)
8. reference: Aigrain & DFM (2022)
9. reference: Aigrain & DFM (2022) ignoring correlated noise accounting for correlated noise
10. reference: Aigrain & DFM (2022)
11. a Gaussian Process is a drop - in replacement for chi - squared
12. more details: Aigrain & Foreman-Mackey (2023) arXiv:2209.08940
13. 7 [1] model building [2] computational cost
14. k(tn , tm ; θ) “kernel” or “covariance”
16. import george import celerite import tinygp
17. my f i rst try: george 1
18. import numpy as np def log_likelihood(params, x, diag, r) : K = build_kernel_matrix(params, x, diag) gof = r.T @ np.linalg.solve(K, r) norm = np.linalg.slogdet(K)[1] return -0.5 * (gof + norm)
19. import numpy as np def log_likelihood(params, x, diag, r) : K = build_kernel_matrix(params, x, diag) gof = r.T @ np.linalg.solve(K, r) norm = np.linalg.slogdet(K)[1] return -0.5 * (gof + norm)
20. k(tn , tm ; θ) “kernel” or “covariance”
21. from george.kernels import * k1 = 1.5 * ExpSquaredKernel(2.3) k2 = 5.5 * Matern32Kernel(0.1) kernel = 0.5 * (k1 + k2)
22. from george import GP gp = GP(kernel) gp.compute(x, yerr) gp.log_likelihood(y)
23. from george import GP gp = GP(kernel) gp.compute(x, yerr) gp.log_likelihood(y) gp.f i t(y) ???
24. the astronomical Python ecosystem + MANY MORE!
25. * API design (library vs scripts) * don’t reinvent the wheel
27. faster: celerite* 2 * yes, that truly is how you pronounce it…
28. import numpy as np def log_likelihood(params, x, diag, r) : K = build_kernel_matrix(params, x, diag) gof = r.T @ np.linalg.solve(K, r) norm = np.linalg.slogdet(K)[1] return -0.5 * (gof + norm)
29. import numpy as np def log_likelihood(params, x, diag, r) : K = build_kernel_matrix(params, x, diag) gof = r.T @ np.linalg.solve(K, r) norm = np.linalg.slogdet(K)[1] return -0.5 * (gof + norm)
31. “semi/quasi - separable” matrices
32. 102 103 104 105 number of data points [N] 10 5 10 4 10 3 10 2 10 1 100 computational cost [seconds] 1 2 4 8 16 32 64 128 256 direct O(N) 100 101 number o reference: DFM, Agol, Ambikasaran, Angus (2017)
33. 102 103 104 105 number of data points [N] 10 4 10 3 10 2 10 1 100 computational cost [seconds] 1 2 4 8 16 32 64 128 256 O(N) 100 101 number o reference: DFM, Agol, Ambikasaran, Angus (2017)
35. +
36. + + vs
37. * interdisciplinary collaboration * importance of implementation
38. 7 [1] 1 (ish) dimensional input [2] specif i c type of kernel restrictions:
39. modern infrastructure: tinygp 3
40. what’s missing from the astronomical Python ecosystem?
41. 7 [1] differentiable programming [2] hardware acceleration
42. the broader numerical computing Python ecosystem + SO MANY MORE!
43. jax.readthedocs.io
44. import numpy as np def linear_least_squares(x, y) : A = np.vander(x, 2) return np.linalg.lstsq(A, y)[0]
45. import jax.numpy as jnp def linear_least_squares(x, y) : A = jnp.vander(x, 2) return jnp.linalg.lstsq(A, y)[0]
46. import jax.numpy as jnp @jax.jit def linear_least_squares(x, y) : A = jnp.vander(x, 2) return jnp.linalg.lstsq(A, y)[0]
48. tinygp.readthedocs.io
49. the broader numerical computing Python ecosystem + SO MANY MORE!
50. * I <3 JAX * don’t reinvent the wheel
51. the why & how of open software in astrophysics
52. credit: Adrian Price-Whelan / / data: SAO/NASA ADS
57. takeaways
58. open software is foundational to astrophysics research let’s consider & discuss interface design and user interaction leverage existing infrastructure & learn when to start fresh
59. get in touch! dfm.io github.com/dfm