# Publications

Publications by categories in reversed chronological order.

## 2024

- [thesis] Physics-Informed Machine Learning for the Earth Sciences: Applications to Glaciology and Paleomagnetism
*Facundo Sapienza*May 2024 - Differentiable Programming for Differential Equations: A Review
*Facundo Sapienza*, Jordi Bolibar, Frank Schäfer, and 8 more authors*arXiv preprint arXiv:2406.09699*, May 2024The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model’s output. Many scientific models are based on differential equations, where differentiable programming plays a crucial role in calculating model sensitivities, inverting model parameters, and training hybrid models that combine differential equations with data-driven approaches. Furthermore, recognizing the strong synergies between inverse methods and machine learning offers the opportunity to establish a coherent framework applicable to both fields. Differentiating functions based on the numerical solution of differential equations is non-trivial. Numerous methods based on a wide variety of paradigms have been proposed in the literature, each with pros and cons specific to the type of problem investigated. Here, we provide a comprehensive review of existing techniques to compute derivatives of numerical solutions of differential equations. We first discuss the importance of gradients of solutions of differential equations in a variety of scientific domains. Second, we lay out the mathematical foundations of the various approaches and compare them with each other. Third, we cover the computational considerations and explore the solutions available in modern scientific software. Last but not least, we provide best-practices and recommendations for practitioners. We hope that this work accelerates the fusion of scientific models and data, and fosters a modern approach to scientific modelling.

- A virtual solar wind monitor at Mars with uncertainty quantification using Gaussian processesAR Azari, E Abrahams, F Sapienza, and 8 more authors
*Journal of Geophysical Research: Machine Learning and Computation*, May 2024Single spacecraft missions do not measure the pristine solar wind continuously because of the spacecrafts’ orbital trajectory. The infrequent spatiotemporal cadence of measurement fundamentally limits conclusions about solar wind‐magnetosphere coupling throughout the solar system. At Mars, such single spacecraft missions result in limitations for assessing the solar wind’s role in causing lower altitude observations, such as auroral dynamics or atmospheric loss. In this work, we detail the development of a virtual solar wind monitor from the Mars Atmosphere and Volatile Evolution (MAVEN) mission; a single spacecraft. This virtual solar wind monitor provides a continuous estimate of the solar wind upstream from Mars with uncertainties. We specifically employ Gaussian process regression to estimate the upstream solar wind and uncertainty estimations that scale with the data sparsity of our real observations. This proxy enables continuous solar wind estimation at Mars with representative uncertainties for the majority of the time since late 2014. We conclude by discussing suggested uses of this virtual solar wind monitor for statistical studies of the Mars space environment and heliosphere.

## 2023

- Magnetic Field Draping in Induced Magnetospheres: Evidence From the MAVEN Mission to MarsA. R. Azari, E. Abrahams, F. Sapienza, and 8 more authors
*Journal of Geophysical Research: Space Physics*, May 2023Abstract The Mars Atmosphere and Volatile EvolutioN (MAVEN) mission has been orbiting Mars since 2014 and now has over 10,000 orbits which we use to characterize Mars’ dynamic space environment. Through global field line tracing with MAVEN magnetic field data we find an altitude dependent draping morphology that differs from expectations of induced magnetospheres in the vertical ( Mars Sun-state, MSO) direction. We quantify this difference from the classical picture of induced magnetospheres with a Bayesian multiple linear regression model to predict the draped field as a function of the upstream interplanetary magnetic field (IMF), remanent crustal fields, and a previously underestimated induced effect. From our model we conclude that unexpected twists in high altitude dayside draping (>800 km) are a result of the IMF component in the MSO direction. We propose that this is a natural outcome of current theories of induced magnetospheres but has been underestimated due to approximations of the IMF as solely directed. We additionally estimate that distortions in low altitude (<800 km) dayside draping along are directly related to remanent crustal fields. We show dayside draping traces down tail and previously reported inner magnetotail twists are likely caused by the crustal field of Mars, while the outer tail morphology is governed by an induced response to the IMF direction. We conclude with an updated understanding of induced magnetospheres which details dayside draping for multiple directions of the incoming IMF and discuss the repercussions of this draping for magnetotail morphology.

- Quantitative Analysis of Paleomagnetic Sampling StrategiesF. Sapienza, L. C. Gallo, Y. Zhang, and 3 more authors
*Journal of Geophysical Research: Solid Earth*, May 2023Abstract Sampling strategies used in paleomagnetic studies play a crucial role in dictating the accuracy of our estimates of properties of the ancient geomagnetic field. However, there has been little quantitative analysis of optimal paleomagnetic sampling strategies and the community has instead defaulted to traditional practices that vary between laboratories. In this paper, we quantitatively evaluate the accuracy of alternative paleomagnetic sampling strategies through numerical experiments and an associated analytical framework. Our findings demonstrate a strong correspondence between the accuracy of an estimated paleopole position and the number of sites or independent readings of the time-varying paleomagnetic field, whereas larger numbers of in-site samples have a dwindling effect. This remains true even when a large proportion of the sample directions are spurious. This approach can be readily achieved in sedimentary sequences by distributing samples stratigraphically, considering each sample as an individual site. However, where the number of potential independent sites is inherently limited the collection of additional in-site samples can improve the accuracy of the paleopole estimate (although with diminishing returns with increasing samples per site). Where an estimate of the magnitude of paleosecular variation is sought, multiple in-site samples should be taken, but the optimal number is dependent on the expected fraction of outliers. The use of filters based on angular distance helps the accuracy of paleopole estimation, but leads to inaccurate estimates of paleosecular variation. We provide both analytical formulas and a series of interactive Jupyter notebooks allowing optimal sampling strategies to be developed from user-informed expectations.

- Embracing Uncertainty to Resolve Polar Wander: A Case Study of Cenozoic North AmericaL. C. Gallo, M. Domeier, F. Sapienza, and 11 more authors
*Geophysical Research Letters*, May 2023Abstract Our understanding of Earth’s paleogeography relies heavily on paleomagnetic apparent polar wander paths (APWPs), which represent the time-dependent position of Earth’s spin axis relative to a given block of lithosphere. However, conventional approaches to APWP construction have significant limitations. First, the paleomagnetic record contains substantial noise that is not integrated into APWPs. Second, parametric assumptions are adopted to represent spatial and temporal uncertainties even where the underlying data do not conform to the assumed distributions. The consequences of these limitations remain largely unknown. Here, we address these challenges with a bottom-up Monte Carlo uncertainty propagation scheme that operates on site-level paleomagnetic data. To demonstrate our methodology, we present an extensive compilation of site-level Cenozoic paleomagnetic data from North America, which we use to generate a high-resolution APWP. Our results demonstrate that even in the presence of substantial noise, polar wandering can be assessed with unprecedented temporal and spatial resolution.

- Universal Differential Equations for glacier ice flow modellingJ. Bolibar, F. Sapienza, F. Maussion, and 3 more authors
*Geoscientific Model Development*, May 2023Geoscientific models are facing increasing challenges to exploit growing datasets coming from remote sensing. Universal Differential Equations (UDEs), aided by differentiable programming, provide a new scientific modelling paradigm enabling both complex functional inversions to potentially discover new physical laws and data assimilation from heterogeneous and sparse observations. We demonstrate an application of UDEs as a proof of concept to learn the creep component of ice flow, i.e. a nonlinear diffusivity differential equation, of a glacier evolution model. By combining a mechanistic model based on a 2D Shallow Ice Approximation Partial Differential Equation with an embedded neural network, i.e. a UDE, we can learn parts of an equation as nonlinear functions that then can be translated into mathematical expressions. We implemented this modelling framework as ODINN.jl, a package in the Julia programming language, providing high performance, source-to-source automatic differentiation (AD) and seamless integration with tools and global datasets from the Open Global Glacier Model in Python. We demonstrate this concept for 17 different glaciers around the world, for which we successfully recover a prescribed artificial law describing ice creep variability by solving ca 500,000 Ordinary Differential Equations in parallel. Furthermore, we investigate which are the best tools in the scientific machine learning ecosystem in Julia to differentiate and optimize large nonlinear diffusivity UDEs. This study represents a proof of concept for a new modelling framework aiming at discovering empirical laws for large-scale glacier processes, such as the variability of ice creep and basal sliding for ice flow, and new hybrid surface mass balance models.

- Choosing the parameter of the Fermat distance: navigating geometry and noiseFrédéric Chazal, Laure Ferraris, Pablo Groisman, and 3 more authorsMay 2023
The Fermat distance has been recently established as a useful tool for machine learning tasks when a natural distance is not directly available to the practitioner or to improve the results given by Euclidean distances by exploding the geometrical and statistical properties of the dataset. This distance depends on a parameter α that greatly impacts the performance of subsequent tasks. Ideally, the value of α should be large enough to navigate the geometric intricacies inherent to the problem. At the same, it should remain restrained enough to sidestep any deleterious ramifications stemming from noise during the process of distance estimation. We study both theoretically and through simulations how to select this parameter.

## 2022

- Heat engines with single-shot deterministic work extractionFederico Cerisola,
*Facundo Sapienza*, and Augusto J Roncaglia*Physical Review E*, May 2022We introduce heat engines working in the nanoregime that allow one to extract a finite amount of deterministic work. Using the resource theory approach to themodynamics, we show that the efficiency of these cycles is strictly smaller than Carnot’s, and we associate this difference with a fundamental irreversibility that is present in single-shot transformations. When fluctuations in the extracted work are allowed there is a trade-off between their size and the efficiency. As the size of fluctuations increases so does the efficiency and optimal efficiency is attained for unbounded fluctuations, while a certain amount of deterministic work is drawn from the cycle. Finally, we show that when the working medium is composed of many particles, by creating an amount of correlations between the subsystems that scale logarithmically with their number, Carnot’s efficiency can also be approached in the asymptotic limit along with deterministic work extraction.

- An optimization method for paleomagnetic Euler pole analysisLeandro C Gallo,
*Facundo Sapienza*, and Mathew Domeier*Computers & Geosciences*, May 2022Owing to the axial symmetry of the Earth’s magnetic field, paleomagnetic data only directly record the latitudinal and azimuthal positions of crustal blocks in the past, and paleolongitude cannot be constrained. An ability to overcome this obstacle is thus of fundamental importance to paleogeographic reconstruction. Paleomagnetic Euler pole (PEP) analysis presents a unique means to recover such information, but prior implementations of the PEP method have incorporated subjective decisions into its execution, undercutting its fidelity and rigor. Here we present an optimization approach to PEP analysis that addresses some of these deficiencies—namely the objective identification of change-points and small-circle arcs that together approximate an apparent polar wander path. We elaborate on our novel methodology and conduct some experiments with synthetic data to demonstrate its performance. We furthermore present implementations of our methods both as adaptable, stand-alone scripts in Python and as a streamlined interactive workflow that can be operated through a web browser.

- Efficient adjustment sets in causal graphical models with hidden variablesEzequiel Smucler,
*Facundo Sapienza*, and Andrea Rotnitzky*Biometrika*, May 2022We study the selection of adjustment sets for estimating the interventional mean under a point exposure dynamic treatment regime, that is, a treatment rule that depends on the subject’s covariates. We assume a nonparametric causal graphical model with, possibly, hidden variables and at least one adjustment set comprised of observable variables. We provide the definition of a valid adjustment set for a point exposure dynamic treatment regime, which generalizes the existing definition for a static intervention. We show that there exists an adjustment set, referred to as optimal minimal, that yields the nonparametric estimator of the interventional mean with the smallest asymptotic variance among those that are based on observable minimal adjustment sets. An observable minimal adjustment set is a valid adjustment set such that all its variables are observable and the removal of any of its variables destroys its validity. We provide similar optimality results for the class of observable minimum adjustment sets, that is, valid observable adjustment sets of minimum cardinality among the observable adjustment sets. Moreover, we show that if either no variables are hidden or if all the observable variables are ancestors of either treatment, outcome or the variables that are used to decide treatment, a globally optimal adjustment set exists. We provide polynomial-time algorithms to compute the globally optimal, optimal minimal and optimal minimum adjustment sets. Because static interventions can be viewed as a special case of dynamic regimes, all our results also apply for static interventions.

- Nonhomogeneous Euclidean first-passage percolation and distance learningPablo Groisman, Matthieu Jonckheere, and
*Facundo Sapienza**Bernoulli*, May 2022Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of the manifold and the underlying density. We define such a sample distance and prove the convergence, as the sample size goes to infinity, to a macroscopic one that we call Fermat distance as it minimizes a path functional, resembling Fermat principle in optics. The proof boils down to the study of geodesics in Euclidean first-passage percolation for nonhomogeneous Poisson point processes.

## 2019

- Correlations as a resource in quantum thermodynamics
*Facundo Sapienza*, Federico Cerisola, and Augusto J Roncaglia*Nature communications*, May 2019The presence of correlations in physical systems can be a valuable resource for many quantum information tasks. They are also relevant in thermodynamic transformations, and their creation is usually associated to some energetic cost. In this work, we study the role of correlations in the thermodynamic process of state formation in the single-shot regime, and find that correlations can also be viewed as a resource. First, we show that the energetic cost of creating multiple copies of a given state can be reduced by allowing correlations in the final state. We obtain the minimum cost for every finite number of subsystems, and then we show that this feature is not restricted to the case of copies. More generally, we demonstrate that in the asymptotic limit, by allowing a logarithmic amount of correlations, we can recover standard results where the free energy quantifies this minimum cost.

## 2018

- Anhysteretic remanent magnetization: model of grain size distribution of spherical magnetite grainsCarlos A Vasquez,
*Facundo Sapienza*, Agustı́n Somacal, and 1 more author*Studia Geophysica et Geodaetica*, May 2018A phenomenological model based on a linear relationship between the magnetic coercivity field and the reciprocal of the grain diameter is applied to explain the anhysteretic remanent magnetization (ARM) imparted to artificial samples with different concentrations of a very well characterized magnetite powder. By analyses of scanning electron microscopy images, the spherically shaped single domain synthetic magnetite is found to follow a lognormal grain size distribution with 86 nm of mean diameter. The proposed model, fitted to ARM measurements up to a peak alternating field of 100 mT, yields a very good agreement. The coercivity behaviour predicted by micromagnetism theory disagrees with the experimental results of this work. A likely explanation for the discrepancy is that the magnetite particles, which consist of a mixture of grains in coherent rotation and curling modes, produce similar observations as domain processes.

- Weighted Geodesic Distance Following Fermat’s Principle
*Facundo Sapienza*, Pablo Groisman, and Matthieu JonckheereMay 2018We propose a density-based estimator for weighted geodesic distances suitable for data lying on a manifold of lower dimension than ambient space and sampled from a possibly nonuniform distribution. After discussing its properties and implementation, we evaluate its performance as a tool for clustering tasks. A discussion on the consistency of the estimator is also given.

- [thesis] Distancia de Fermat y geodésicas en percolación euclidea: teoría y aplicaciones en Machine Learning
*Facundo Sapienza*Aug 2018

## 2017

- [thesis] Teoría de recursos de la termodinámica cuántica : correlaciones en los procesos de formación de recursos
*Facundo Sapienza*Dec 2017