Solving Einstein’s equations as Bayesian inference

Frederik De Ceuster, Tom Colemont, Tjonnie G.F. Li
Proceedings of the First International Conference on Probabilistic Numerics, PMLR 271:131-137, 2025.

Abstract

Gravitational waves (GWs) are revolutionising our fundamental understanding of physics and cosmology. However, the numerical modelling required to turn their measurements into scientific detections poses a formidable computational challenge. In this paper, we explore the feasibility of probabilistic numerics (PN) to model GW sources. As a proof-of-principle, we pose the solution of the Einstein equations, which relate the dynamics of spacetime to its matter content, as a Bayesian inference problem. Using a fixed-point iteration scheme and iterative linearisation, we show that the non-linear problem can be divided into a set of consecutively solvable Bayesian linear regression problems. As a first application, we use this approach to solve the spacetime geometry inside a static and spherically-symmetric neutron star. We conclude that PN provides a promising approach to overcome some of the computational challenges in GW science.

Cite this Paper

BibTeX
@InProceedings{pmlr-v271-ceuster25a, title = {Solving {E}instein’s equations as {B}ayesian inference}, author = {Ceuster, Frederik De and Colemont, Tom and Li, Tjonnie G.F.}, booktitle = {Proceedings of the First International Conference on Probabilistic Numerics}, pages = {131--137}, year = {2025}, editor = {Kanagawa, Motonobu and Cockayne, Jon and Gessner, Alexandra and Hennig, Philipp}, volume = {271}, series = {Proceedings of Machine Learning Research}, month = {01--03 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v271/main/assets/ceuster25a/ceuster25a.pdf}, url = {https://proceedings.mlr.press/v271/ceuster25a.html}, abstract = {Gravitational waves (GWs) are revolutionising our fundamental understanding of physics and cosmology. However, the numerical modelling required to turn their measurements into scientific detections poses a formidable computational challenge. In this paper, we explore the feasibility of probabilistic numerics (PN) to model GW sources. As a proof-of-principle, we pose the solution of the Einstein equations, which relate the dynamics of spacetime to its matter content, as a Bayesian inference problem. Using a fixed-point iteration scheme and iterative linearisation, we show that the non-linear problem can be divided into a set of consecutively solvable Bayesian linear regression problems. As a first application, we use this approach to solve the spacetime geometry inside a static and spherically-symmetric neutron star. We conclude that PN provides a promising approach to overcome some of the computational challenges in GW science.} }
Endnote
%0 Conference Paper %T Solving Einstein’s equations as Bayesian inference %A Frederik De Ceuster %A Tom Colemont %A Tjonnie G.F. Li %B Proceedings of the First International Conference on Probabilistic Numerics %C Proceedings of Machine Learning Research %D 2025 %E Motonobu Kanagawa %E Jon Cockayne %E Alexandra Gessner %E Philipp Hennig %F pmlr-v271-ceuster25a %I PMLR %P 131--137 %U https://proceedings.mlr.press/v271/ceuster25a.html %V 271 %X Gravitational waves (GWs) are revolutionising our fundamental understanding of physics and cosmology. However, the numerical modelling required to turn their measurements into scientific detections poses a formidable computational challenge. In this paper, we explore the feasibility of probabilistic numerics (PN) to model GW sources. As a proof-of-principle, we pose the solution of the Einstein equations, which relate the dynamics of spacetime to its matter content, as a Bayesian inference problem. Using a fixed-point iteration scheme and iterative linearisation, we show that the non-linear problem can be divided into a set of consecutively solvable Bayesian linear regression problems. As a first application, we use this approach to solve the spacetime geometry inside a static and spherically-symmetric neutron star. We conclude that PN provides a promising approach to overcome some of the computational challenges in GW science.
APA
Ceuster, F.D., Colemont, T. & Li, T.G.. (2025). Solving Einstein’s equations as Bayesian inference. Proceedings of the First International Conference on Probabilistic Numerics, in Proceedings of Machine Learning Research 271:131-137 Available from https://proceedings.mlr.press/v271/ceuster25a.html.

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