arXiv subjects

Joseph Janssen

Publications and source records attributed to Joseph Janssen.

8 recordsLinked to original sources

arXiv2026

On the Adversarial Robustness of Hydrological Models

The evaluation of hydrological models is essential for both model selection and reliability assessment. However, simply comparing predictions to observations is insufficient for understanding the global landscape of model behavior. This is especially true for many deep learning models, whose structures are complex. Further, in risk-averse operational settings, water managers require models that are trustworthy and provably safe, as non-robustness can put our critical infrastructure at risk. Motivated by the need to select reliable models for operational deployment, we introduce and explore adversarial robustness analysis in hydrological modeling, evaluating whether small, targeted perturbations to meteorological forcings induce substantial changes in simulated discharge. We compare physical-conceptual and deep learning-based hydrological models across 1,347 German catchments under perturbations of varying magnitudes, using the fast gradient sign method (FGSM). We find that, as expected, the FGSM perturbations systematically reduce KGE and increase MSE. However, catastrophic failure is rare and, surprisingly, LSTMs generally demonstrate greater robustness than HBV models. Further, changes in both the predicted hydrographs and the internal model states often respond approximately linearly (at least locally) as perturbation size increases, providing a compact summary of how errors grow under such perturbations. Similar patterns are also observed for random perturbations, suggesting that small input changes usually introduce approximately proportional changes in model output. Overall, these findings support further consideration of LSTMs for operational deployment (due both to their predictive power and robustness), and motivate future work on both characterizing model responses to input changes and improving robustness through architectural modifications and training design.

physics.geo-ph↗

arXiv2025

Gradient-flow SDEs have unique transient population dynamics

Identifying the drift and diffusion of an SDE from its population dynamics is a notoriously challenging task. Researchers in machine learning and single-cell biology have only been able to prove a partial identifiability result: for potential-driven SDEs, the gradient-flow drift can be identified from temporal marginals if the Brownian diffusivity is already known. Existing methods therefore assume that the diffusivity is known a priori, despite it being unknown in practice. We dispel the need for this assumption by providing a complete characterization of identifiability: the gradient-flow drift and Brownian diffusivity are jointly identifiable from temporal marginals if and only if the process is observed outside of equilibrium. Given this fundamental result, we propose nn-APPEX, the first Schrodinger Bridge-based inference method that can simultaneously learn the drift and diffusion of a gradient-flow SDE solely from observed marginals. Extensive experiments show that nn-APPEX's ability to adjust its diffusion estimate enables accurate inference, while previous Schrodinger Bridge methods obtain biased drift estimates due to their assumed, and likely incorrect, diffusion.

math.PR↗

arXiv2024

Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE from data is a challenging task, especially if individual trajectories are not observable. Motivated by burgeoning research in single-cell datasets, we present the first comprehensive approach for jointly identifying the drift and diffusion of an SDE from its temporal marginals. Assuming linear drift and additive diffusion, we show that non-identifiability can only arise if the initial distribution possesses generalized rotational symmetries. We further prove that even if this condition holds, the drift and diffusion can almost always be recovered from the marginals. Additionally, we show that the causal graph of any SDE with additive diffusion can be recovered from the identified SDE parameters. To complement this theory, we adapt entropy-regularized optimal transport to handle anisotropic diffusion, and introduce APPEX (Alternating Projection Parameter Estimation from $X_0$), an iterative algorithm designed to estimate the drift, diffusion, and causal graph of an additive noise SDE, solely from temporal marginals. We show that APPEX iteratively decreases Kullback-Leibler divergence to the true solution, and demonstrate its effectiveness on simulated data from linear additive noise SDEs.

stat.ML↗

arXiv2024

Tackling water table depth modeling via machine learning: From proxy observations to verifiability

Spatial patterns of water table depth (WTD) play a crucial role in shaping ecological resilience, hydrological connectivity, and human-centric systems. Generally, a large-scale (e.g., continental or global) continuous map of static WTD can be simulated using either physically-based (PB) or machine learning-based (ML) models. We construct three fine-resolution (500 m) ML simulations of WTD, using the XGBoost algorithm and more than 20 million real and proxy observations of WTD, across the United States and Canada. The three ML models were constrained using known physical relations between WTD's drivers and WTD and were trained by sequentially adding real and proxy observations of WTD. Through an extensive (pixel-by-pixel) evaluation across the study region and within ten major ecoregions of North America, we demonstrate that our models (corr=0.6-0.75) can more accurately predict unseen real and proxy observations of WTD compared to two available PB simulations of WTD (corr=0.21-0.40). However, we still argue that currently-available large-scale simulations of static WTD could be uncertain within data-scarce regions such as steep mountainous regions. We reason that biased observational data mainly collected from low-elevation floodplains and the over-flexibility of available models can negatively affect the verifiability of large-scale simulations of WTD. Ultimately, we thoroughly discuss future directions that may help hydrogeologists decide how to improve machine learning-based WTD estimations. In particular, we advocate for the use of proxy satellite data, the incorporation of physical laws, the implementation of better model verification standards, the development of novel globally-available emergent indices, and the collection of more reliable observations.

cs.LG↗

arXiv2023

A Gaussian Sliding Windows Regression Model for Hydrological Inference

Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes in streamflow is of high practical importance. Since water can take a variety of flow paths to generate streamflow, a series of distinct runoff pulses may combine to create the observed streamflow time series. Current state-of-the-art models are not able to sufficiently confront the problem complexity with interpretable parametrization, thus preventing novel insights about the dynamics of distinct flow paths from being formed. The proposed Gaussian Sliding Windows Regression Model targets this problem by combining the concept of multiple windows sliding along the time axis with multiple linear regression. The window kernels, which indicate the weights applied to different time lags, are implemented via Gaussian-shaped kernels. As a result, straightforward process inference can be achieved since each window can represent one flow path. Experiments on simulated and real-world scenarios underline that the proposed model achieves accurate parameter estimates and competitive predictive performance, while fostering explainable and interpretable hydrological modeling.

stat.ME↗

arXiv2023

How to out-perform default random forest regression: choosing hyperparameters for applications in large-sample hydrology

Predictions are a central part of water resources research. Historically, physically-based models have been preferred; however, they have largely failed at modeling hydrological processes at a catchment scale and there are some important prediction problems that cannot be modeled physically. As such, machine learning (ML) models have been seen as a valid alternative in recent years. In spite of their availability, well-optimized state-of-the-art ML strategies are not being widely used in water resources research. This is because using state-of-the-art ML models and optimizing hyperparameters requires expert mathematical and statistical knowledge. Further, some analyses require many model trainings, so sometimes even expert statisticians cannot properly optimize hyperparameters. To leverage data and use it effectively to drive scientific advances in the field, it is essential to make ML models accessible to subject matter experts by improving automated machine learning resources. ML models such as XGBoost have been recently shown to outperform random forest (RF) models which are traditionally used in water resources research. In this study, based on over 150 water-related datasets, we extensively compare XGBoost and RF. This study provides water scientists with access to quick user-friendly RF and XGBoost model optimization.

stat.AP↗

arXiv2023

Learning from limited temporal data: Dynamically sparse historical functional linear models with applications to Earth science

Scientists and statisticians often want to learn about the complex relationships that connect two time-varying variables. Recent work on sparse functional historical linear models confirms that they are promising for this purpose, but several notable limitations exist. Most importantly, previous works have imposed sparsity on the historical coefficient function, but have not allowed the sparsity, hence lag, to vary with time. We simplify the framework of sparse functional historical linear models by using a rectangular coefficient structure along with Whittaker smoothing, then reduce the assumptions of the previous frameworks by estimating the dynamic time lag from a hierarchical coefficient structure. We motivate our study by aiming to extract the physical rainfall-runoff processes hidden within hydrological data. We show the promise and accuracy of our method using eight simulation studies, further justified by two real sets of hydrological data.

stat.ME↗

arXiv2022

Ultra-marginal Feature Importance: Learning from Data with Causal Guarantees

Scientists frequently prioritize learning from data rather than training the best possible model; however, research in machine learning often prioritizes the latter. Marginal contribution feature importance (MCI) was developed to break this trend by providing a useful framework for quantifying the relationships in data. In this work, we aim to improve upon the theoretical properties, performance, and runtime of MCI by introducing ultra-marginal feature importance (UMFI), which uses dependence removal techniques from the AI fairness literature as its foundation. We first propose axioms for feature importance methods that seek to explain the causal and associative relationships in data, and we prove that UMFI satisfies these axioms under basic assumptions. We then show on real and simulated data that UMFI performs better than MCI, especially in the presence of correlated interactions and unrelated features, while partially learning the structure of the causal graph and reducing the exponential runtime of MCI to super-linear.

stat.ML↗