Las Catalinas, Guanacaste, Costa Rica; NOVEMBER 7-9, 2022

Math+X_2022 logo

The analysis of planet formation and evolution has moved beyond an era focused on dynamics of accretion followed by secular cooling and has progressed to an era where coupling between physical processes and material properties at extreme conditions is considered. In this coupling lie opportunities, with possible underlying models, for the analysis of inverse problems and deep learning to constrain these material properties and further reveal these processes. Modeling the formation, evolution, interior structure, and magnetic fields of the diversity of exoplanets depends fundamentally on the EOS, chemistry, and optical and transport properties of the constituent materials under WDM conditions. A central role is played by liquid metallic hydrogen and ionized H2O in gas and ice giants.

While the study of the metallic phase transition remains challenging, supervised learning with deep neural networks has been employed to identify EOS (from final-state particle spectra) in QCD. Moreover, deep learning is already employed in condensed matter physics. It has been shown that deep neural networks can be integrated into, or fully replace, the Kohn-Sham density functional theory scheme for multi-electron systems in simple harmonic oscillator and random external potentials. At the same time, the physical properties and phase diagrams of the mentioned ice compounds at high pressures are still a main subject of research.

Inside our solar system, extreme conditions also exist in the interiors of ice giants, Neptune and Uranus, and gas giants, Saturn and Jupiter. In Saturn and Jupiter the mentioned metallic phase transitions occur. Not only hydrogen, but also helium, in quite recent work, has been shown to behave as a metal at least at the highest pressures encountered in Jupiter and perhaps over a wider range of pressures in the many, often much hotter, planets of Jupiter’s mass and larger that are now apparently common in the universe. Of particular relevance to gas-giant evolution, is their specific heat and hydrogen/helium immiscibility curve. These are accessible via the above mentioned theoretical and experimental techniques of HEDP studies. Recent and past measurements of the higher gravitational moments of Jupiter and Saturn via the Juno mission and the Cassini Grand Finale, provide planetary density-profile data of unprecedented character. Also, the rings of Saturn and Uranus may act as seismographs, recording gravitational perturbations associated with acoustic oscillation modes of the planet. Moreover, Doppler imaging from spacecrafts for “helio”seismology on giant planets holds great promise. These data, along with high-pressure EOS data and benchmarked theory for planetary materials from HEDP laboratory studies may provide key constraints for new models of solar systems and exoplanets.

Connecting observations for Jupiter and Saturn, Uranus and Neptune, and assimilating data from exoplanets, experimental data and theoretical formulations, directly (physical properties) and indirectly (coupling to processes), naturally belongs to the fields of (initially idealized) inverse problems and deep learning. This Symposium aims to break new ground in these connections.

Invited Speakers:

Solar System Giants and Exoplanets

Tristan Guillot (Observatoire de la Côte d’Azur)
Burkhard Militzer (UC Berkeley)
David Stevenson (Caltech) KEYNOTE
Daniel Thorngren (Johns Hopkins)

Matter Under Extreme Conditions

Roberto Car (Princeton) KEYNOTE
Carlo Pierleoni (Rome)
Chris Pickard (Cambridge) KEYNOTE

Inverse Problems

Pedro Caro (BCAM)
Joonas Ilmavirta (University of Jyväskylä)
Matti Lassas (Helsinki)
Qin Li (Wisconsin-Madison)
Lauri Oksanen (Helsinki)

Scientific Machine Learning

Ivan Dokmanić (Basel)
Carlos Fernandez-Granda (NYU)
Samory Kpotufe (Columbia)
Stéphane Mallat (Collège de France) KEYNOTE
Santiago Segarra (Rice)
Soledad Villar (Johns Hopkins)

Proof of vaccination required
Travel Information:

Hotel: Santarena Hotel
Nearest Airport: Liberia (LIR), Costa Rica
Las Catalinas Map

The entire hotel is booked for the Symposium. In Costa Rica, there is a vaccination mandate for all the hotel staff, which will be verified. Liberia airport has a COVID-19 testing center; testing takes an hour and is provided prior to checkin for return flights. Prearranged vaccinated drivers will pick up the participants in disinfected cars from Liberia airport.

funded by
Simons Foundation logo

MATH + X Program

This workshop is funded by the Simons Foundation under the MATH + X program: encouraging novel collaborations between mathematics and other disciplines in science and engineering.

2020 Math + X Symposium on Inverse Problems and Deep Learning, Mitigating Natural Hazards

2019 Math + X Symposium on Inverse Problems and Deep Learning in Space Exploration

2018 Math + X Symposium on Data Science and Inverse Problems in Geophysics

2017 Math + X Symposium on Seismology and Inverse Problems

Organizing Committee:

Joan Bruna (NYU)
David Ceperley (UIUC)
Chair: Maarten de Hoop (Rice University)
Paul Johnson (LANL)
Gunther Uhlmann (University of Washington, HKUST)
Robert van der Hilst  (MIT)
Benjamin Weiss  (MIT)

in collaboration with:
Esteban Chaves (Universidad Nacional Costa Rica)