arXiv subjects

Victor Boussange

Publications and source records attributed to Victor Boussange.

6 recordsLinked to original sources

arXiv2026

Temporal horizons in forecasting: a performance-learnability trade-off

When training autoregressive models to forecast dynamical systems, a critical question arises: how far into the future should the model be trained to predict for optimal performance? In this work, we address this question by analyzing the relationship between the geometry of the loss landscape and the training time horizon. Using dynamical systems theory, we prove that loss minima for long horizons generalize well to short-term forecasts, whereas minima found on short horizons result in worse long-term predictions. However, we also prove that the loss landscape becomes rougher as the training horizon grows, making long-horizon training inherently challenging. We validate our theory through numerical experiments and discuss practical implications for selecting training horizons. Our results provide a principled foundation for hyperparameter optimization in autoregressive forecasting models.

cs.LG↗

arXiv2026

Multi-scale species richness estimation with deep learning

Biodiversity assessments depend critically on the spatial scale at which species richness is measured. How species richness accumulates with sampling area is influenced by natural and anthropogenic processes whose effects vary across spatial scales. These accumulation dynamics, described by the species-area relationship (SAR), are challenging to assess because most biodiversity surveys cover sampling areas far smaller than the scales at which these processes operate. Here, we combine sampling theory with deep learning to estimate species richness at arbitrary spatial scales across geographic space from existing ecological surveys. We apply our model, named MuScaRi, to ~350k vegetation surveys across Europe. Validated against independent regional plant inventories, MuScaRi reduces root mean squared error of vascular plant richness estimates by 61% relative to conventional estimators, yields substantially less biased predictions, and produces multi-scale richness maps alongside spatially explicit estimates of the species accumulation rate, a key indicator for biodiversity conservation. By encompassing the full spectrum of ecologically relevant spatial scales within a single unified framework, MuScaRi provides an essential tool for robust biodiversity assessments and forecasts under global change.

q-bio.PE↗

arXiv2025

Differentiable Programming for Differential Equations: A Review

The 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.

math.NA↗

arXiv2024

Chaotic Slow Slip Events in New Zealand from two coupled slip patches: a proof of concept

Recent studies showed that seemingly random Slow Slip Events (SSEs) can display chaotic patterns within the largest source of seismic hazards in New Zealand, the Hikurangi subduction zone. Some irregular SSE occurrences are therefore not arbitrary but behave with short-term predictability. However, the forecasting challenge persists as observations remain too short and noisy to constrain purely data-driven solutions, calling for a physics-based modelling approach. Here we propose a physical model of two coupled oscillators, each capturing the behaviour of a single slow-slip patch, for the deep Kaimanawa and the shallow East Coast SSEs respectively. The simplified model successfully reproduces the type of chaotic behaviour observed at the Global Navigational Satellite System station in Gisborne, yielding SSEs of appropriately varying amplitude and duration. Those results reveal that the multi-physics response of the shear zone strongly controls the underlying system, even before accounting for any geometrical complexity or distribution of material properties.

physics.geo-ph↗

arXiv2023

Processes analogous to ecological interactions and dispersal shape the dynamics of economic activities

The processes of ecological interactions, dispersal and mutations shape the dynamics of biological communities, and analogous eco-evolutionary processes acting upon economic entities have been proposed to explain economic change. This hypothesis is compelling because it explains economic change through endogenous mechanisms, but it has not been quantitatively tested at the global economy level. Here, we use an inverse modelling technique and 59 years of economic data covering 77 countries to test whether the collective dynamics of national economic activities can be characterised by eco-evolutionary processes. We estimate the statistical support of dynamic community models in which the dynamics of economic activities are coupled with positive and negative interactions between the activities, the spatial dispersal of the activities, and their transformations into other economic activities. We find strong support for the models capturing positive interactions between economic activities and spatial dispersal of the activities across countries. These results suggest that processes akin to those occurring in ecosystems play a significant role in the dynamics of economic systems. The strength-of-evidence obtained for each model varies across countries and may be caused by differences in the distance between countries, specific institutional contexts, and historical contingencies. Overall, our study provides a new quantitative, biologically inspired framework to study the forces shaping economic change.

econ.EM↗

arXiv2022

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately account for certain non-local phenomena such as, e.g., interactions at a distance. In order to properly capture these phenomena non-local nonlinear PDE models are frequently employed in the literature. In this article we propose two numerical methods based on machine learning and on Picard iterations, respectively, to approximately solve non-local nonlinear PDEs. The proposed machine learning-based method is an extended variant of a deep learning-based splitting-up type approximation method previously introduced in the literature and utilizes neural networks to provide approximate solutions on a subset of the spatial domain of the solution. The Picard iterations-based method is an extended variant of the so-called full history recursive multilevel Picard approximation scheme previously introduced in the literature and provides an approximate solution for a single point of the domain. Both methods are mesh-free and allow non-local nonlinear PDEs with Neumann boundary conditions to be solved in high dimensions. In the two methods, the numerical difficulties arising due to the dimensionality of the PDEs are avoided by (i) using the correspondence between the expected trajectory of reflected stochastic processes and the solution of PDEs (given by the Feynman-Kac formula) and by (ii) using a plain vanilla Monte Carlo integration to handle the non-local term. We evaluate the performance of the two methods on five different PDEs arising in physics and biology. In all cases, the methods yield good results in up to 10 dimensions with short run times. Our work extends recently developed methods to overcome the curse of dimensionality in solving PDEs.

math.NA↗