arXiv subjects

Florian Huber

Publications and source records attributed to Florian Huber.

At least 19 recordsLinked to original sources

arXiv2026

Fluctuation Correction and Global Solutions for the Stochastic Shigesada-Kawasaki-Teramoto System via Entropy-Based Regularization

We study a stochastic extension of the n-species Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system, in which a multiplicative noise term accounts for fluctuation corrections to the mean-field dynamics arising from a finite underlying population. The noise we consider is motivated by, but not rigorously derived from, the particle-system approximation of Chen, Daus, Holzinger, and J"ungel; it only partially respects the entropy (gradient-flow) structure of the deterministic system, which is the main source of the technical difficulties addressed in this paper. For the resulting system of stochastic partial differential equations (SPDEs), we establish the existence of nonnegative, global, weak martingale solutions, under a detailed-balance condition on the diffusion coefficients and a smallness condition relating the noise intensity to these coefficients. This smallness condition amounts to a sufficiently large population size N (equivalently, small fluctuation strength 1/N): the existence theory thus operates in the perturbative regime around the deterministic mean-field limit, and for fixed coefficients it is always satisfiable once N is large enough.

math.PR↗

arXiv2026

Weak and strong discretization errors for signatures of Gaussian processes

Let $X$ be a continuous Gaussian process in $\mathbb{R}^d$, $d\ge2$, with independent components of roughness $H\in(\tfrac14,1)$, possibly with a linear drift, and let $X^n$ be its piecewise-linear interpolant on a mesh of width $δ$. We study how well the truncated signature of $X^n$ approximates that of the natural lift of $X$, in mean (the weak error) and in $L^2$ (the strong error). Over a class of drivers defined by quantitative regularity conditions, the weak error at every fixed truncation level is $O(δ^{γ(H)})$ with $γ(H)=\min(2H,4H-1)$, uniformly over the class, and for truncation levels $M\ge4$ fractional Brownian motion attains this rate. For centred drivers the weak error vanishes at levels $1$ to $3$, Gaussian or not. It first appears at level~$4$, where we compute its leading constant for independent fractional Brownian motion in $d=2$: on $(\tfrac12,1)$ it is $1/(2\sqrt3)$, independent of $H$, and on $(\tfrac14,\tfrac12)$ it is given by a $ζ$-series. For fractional Brownian motion with drift, a level-$3$ error of the same order appears for $H\ge\tfrac12$. Below $\tfrac12$ the drift reaches the rate only at levels $\ge5$ (proved for $d\ge3$). The strong error is of exact order $δ^{2H-1/2}$ for fractional Brownian motion with $H\in(\tfrac12,1)$, so in mean square the weak error lies a full power of $δ$ below it. For $H\le\tfrac12$ the strong error is $O(δ^{\vartheta})$ for every $\vartheta<2H-\tfrac12$, uniformly over the class, and the exponent $2H-\tfrac12$ cannot be improved. Finally, we construct pairs of laws in the class whose mesh data have the same law but whose expected signatures differ by order $δ^{γ(H)}$. Hence no quantity computed from the mesh data has mean within $o(δ^{γ(H)})$ of the expected signature uniformly over the class.

math.PR↗

arXiv2026

Gaussian fluctuations of the moderately interacting Shigesada-Kawasaki-Teramoto particle system around the mollified mean-field limit

We study, at the logarithmic mollification scale $η^{-2(d+1+α)}\leδ\log N$ of Chen, Daus, Holzinger and J{ü}ngel, the fluctuation field $V^N=\sqrt N(μ^N-u_η)$ of the moderately interacting multi-species particle system whose mean-field limit is the Shigesada- Kawasaki-Teramoto (SKT) cross-diffusion system. The field is centred at the solution $u_η$ of the mollified equation, which depends on $N$ through $η$. On a scale of weighted Bessel-potential spaces of negative order we prove that the laws of $(V^N,M^N)$ are tight, where $M^N$ is the martingale part. Every limit point of $M^N$ is a continuous Gaussian martingale with an explicit deterministic bracket. Every limit point of $V^N$ is a weak solution, and the mild solution, of a linear Ornstein-Uhlenbeck SPDE whose drift is the linearisation of the SKT operator at the limit $u$. The initial field and the martingale are independent, and weak solutions are unique given both, so the whole sequence converges in law, jointly with the martingale part, and the limit is unique in law among solutions of the martingale problem. The noise is $d M_i=div(\sqrt{2u_iΘ_i}dW_i)$, with $Θ_i=σ_i+\sum_jf(a_{ij}u_j)$ and $W$ a cylindrical Wiener process on $L^2(\mathbb{R}^d;\mathbb{R}^{nd})$. The hypotheses are those of Chen, Daus, Holzinger and J{ü}ngel, including the smallness and the nonnegativity on $\mathbb{R}$ of the nonlinearity $f$. We add radial kernels $B_{ij}$, the independence of the initial data and the Brownian motions across particles and species, a smaller $δ$, a regularity budget on $u_0$, a strengthened smallness condition on $f$ that makes the backward system diagonally dominant in weighted spaces, and an integer Sobolev index $s$.

math.PR↗

arXiv2026

Systems of rough stochastic differential equations I: weak existence and Yamada--Watanabe

For systems of rough stochastic differential equations in the sense of Friz--Hocquet--Lê, with a fixed deterministic rough driver, we prove two results. The first is weak existence with unbounded coefficients. The Itô data is assumed continuous and of linear growth, with no Hölder or Lipschitz continuity and no ellipticity. The rough vector field is a controlled pair of linear growth with bounded derivatives, subject either to a norm-curvature decay or to diagonality with coordinatewise curvature decay; in the diagonal case a coordinatewise upper bound on the diffusion matrix is added. The existing results ask the Itô data and the rough field to be bounded. We remove that boundedness, and ask in exchange for a curvature hypothesis on the rough field, bounds on its derivatives, and a narrower index configuration. The conclusion is weaker on two counts: the bounds that define a solution are imposed in the mean rather than uniformly on the probability space, and the solution's moments stop at the order the initial law carries. The second is the Yamada--Watanabe implication for rough equations: weak existence, together with pathwise uniqueness, yields a strong solution and joint uniqueness in law. A solution here is not defined by a pathwise identity but by two bounds on a remainder, one of them conditional, and an arbitrary enlargement of the filtration need not preserve that one. The enlargements the Yamada--Watanabe construction produces are immersions, however, and along an immersion both bounds transfer unchanged.

math.PR↗

arXiv2026

Beyond Aggregate VARs: A Bayesian Benchmark for HANK Models

Heterogeneous-agent New Keynesian (HANK) models characterize how entire cross-sectional distributions respond to structural shocks. Traditional representative-agent models are routinely disciplined by impulse responses from aggregate vector autoregressions (VARs). HANK models have no comparable established empirical benchmark because they make predictions not only about aggregates, but also about distributions of micro-level data. We propose a Bayesian benchmark that jointly models macroeconomic aggregates and several marginal distributions from repeated cross sections, including distributions observed in different surveys. Our approach can use both standard structural VAR identification approaches on macroeconomic aggregates and identification restrictions imposed on micro-level data. The model delivers a joint posterior of the distributional effects of shocks, without the need for household panel data or a separate first-stage density estimate.

econ.EM↗

arXiv2026

Clustered Local Projections for Short and Ultra-Short Time Series -- A Hierarchical Bayesian Framework

Estimating the dynamic effects of economic shocks in short and very short samples is impeded by a lack of degrees of freedom. We offer a solution based on a Bayesian hierarchical framework for estimating local projection (LP) impulse response functions across a panel of related time series. The framework explicitly accommodates unbalanced panels in which some series are substantially shorter than others, allowing the short series to borrow information from longer ones at horizons where the short series carry little or no own data. Since series might exhibit heterogeneous dynamics, we develop a sparse finite mixture pool that clusters units by similarity of their impulse response profiles. We show in simulations that our approach substantially improves LP estimation accuracy relative to the standard approach if the time series are short while producing similar LPs for longer time series. Using a US price dataset, augmented with survey responses, we find that supply-chain and oil shocks trigger heterogeneous reactions of different price measures, with headline price indices responding more sharply than their core counterparts and goods prices changing more than services prices.

econ.EM↗

arXiv2026

Soft-Noncrossing Bayesian Panel Quantile Regression for Measuring Climate Tail Risk

We develop a hierarchical Bayesian panel quantile regression model in which unit-specific coefficient paths are smoothed across quantiles by Gaussian processes, while a common time effect absorbs aggregate shocks. Componentwise-monotone Bernstein polynomials, perturbed by unit-specific deviations, deliver soft noncrossing, and we provide identification conditions together with a bound on the crossing probability. Applying the model to 33 countries over 1979--2023, we find that global temperature shocks generate a systemic, non-diversifiable downside risk to output growth. This risk is concentrated in the lower tail and disproportionately affects emerging markets. Finally, we apply our framework to risk analysis and show that the model reduces out-of-sample tail-risk forecast loss by roughly one-third relative to country-specific quantile regressions.

econ.EM↗

arXiv2026

Markovian Lifts of Stochastic Volterra Equations in Sobolev Spaces: Solution theory, an Ito Formula and Invariant Measures

We investigate Markovian lifts of stochastic Volterra equations (SVEs) with completely monotone kernels and general coefficients within the framework of weighted Sobolev spaces. Our primary focus is developing a comprehensive solution theory for a class of non-local stochastic evolution equations (SEEs) encompassing these Markovian lifts. This enables us to provide conditions for the existence of invariant measures for the lifted processes and the corresponding SVE, and, for uniformly elliptic diffusion coefficients, to establish uniqueness and exponential ergodicity via a generalized Harris theorem. Another key contribution is an It^o-type formula for the stochastic Volterra equations under consideration, from which we develop a range of applications: a finite-time blow-up criterion, a Feynman-Kac representation together with the associated backward Kolmogorov equation on the lift space, and a pricing equation for rough volatility models.

math.PR↗

arXiv2026

A Flexible Approach to Augmenting a Bayesian VAR with Nonlinear Factors

This paper proposes a vector autoregression augmented with nonlinear factors that are modeled nonparametrically using regression trees. There are four main advantages of our model. First, the use of factor methods ensures that departures from linearity are modeled parsimoniously. In particular, they exhibit functional pooling where a small number of nonlinear factors are used to model common nonlinearities across variables. Second, modeling potential nonlinearities nonparametrically lessens the risk of misspecification. Third, Bayesian computation using MCMC is straightforward even in very high-dimensional models, allowing for efficient, equation-by-equation estimation, thus avoiding computational bottlenecks that arise in popular alternatives such as the time-varying parameter VAR. Fourth, existing methods for identifying structural economic shocks in linear factor models can be adapted for the nonlinear case in a straightforward fashion using our model. Exercises involving artificial and macroeconomic data illustrate the properties of our model and its usefulness for forecasting and structural economic analysis.

econ.EM↗

arXiv2026

General Seemingly Unrelated Local Projections

We develop a flexible framework for Bayesian estimation of impulse responses using Local Projections (LPs) with instrumental variables. It accommodates multiple shocks and instruments, accounts for autocorrelation in multi-step forecasts by jointly modeling all LPs as a seemingly unrelated system of equations, defines a flexible yet parsimonious joint prior for impulse responses based on a Gaussian Process, and allows for joint inference about the entire vector of impulse responses. We show via Monte Carlo simulations that our approach delivers more accurate point and uncertainty estimates than standard methods. To address misspecification, we propose an optional robustification step based on power posteriors.

econ.EM↗

arXiv2026

AI-Guided Design and Optimization of Graphite-Based Anodes via Iterative Experimental Feedback

This study presents an iterative AI-guided workflow that accelerates graphite-based anode development by improving both formulation feasibility and process robustness. Sequential learning via AI/ML-guided multiobjective inverse design for anode optimization was implemented using the Citrine Platform. Starting from a noisy, incomplete dataset, the Citrine Platform was used to generate early surrogate models, which despite low predictive certainty highlighted missing process constraints. By iteratively adding feasibility labels and boundary condition failures, the workflow rapidly converged toward manufacturable, higher-performing formulations. Fabrication reliability improved from frequent process failures to 100% successful cell production, while the fraction of cells delivering $\geq$ 350 mAh g$^{-1}$ increased from 28.4% to 84.8%, with capacity retention rising from 42.1% to 97.3%. These results demonstrate that structured, feedback-driven AI workflows can transform imperfect industrial data into actionable guidance, enabling faster, more reproducible optimization of battery electrode manufacturing.

cs.LG↗

arXiv2026

Double Descent and Benign Overfitting in Macroeconomic Forecasting

We study double descent and benign overfitting in macroeconomic forecasting. We document that double-descent risk curves arise in standard macroeconomic datasets that are driven by a small number of latent factors, and we characterize when the underlying benign-overfitting mechanism holds. The conditions of Bartlett et al. (2020) are satisfied under the exact factor model and can also hold under the more realistic approximate factor model, provided idiosyncratic variances are not too dispersed across series. Because macroeconomic panels have only moderate dimensions, the overparameterization ratio N/T required by the theory is not naturally available. Our solution is to augment the data with synthetic copies from an estimated factor model and we prove that this strategy converges to a kernel ridge regression with a factor-structured kernel. Using monthly (FRED-MD) and quarterly (FRED-QD) US data, the resulting estimator consistently outperforms the Stock-Watson factor model for point forecasting across all series and horizons, with gains that are pervasive, statistically significant, and increasing with the forecast horizon. Our results suggest that benign overfitting, when it works, succeeds because overparameterization implicitly constructs a well-behaved kernel, not because overparameterization is intrinsically desirable.

econ.EM↗

arXiv2025

Coarsened Bayesian VARs -- Correcting BVARs for Incorrect Specification

Model misspecification in multivariate econometric models can strongly influence estimates of quantities of interest such as structural parameters, forecast distributions or responses to structural shocks, even more so if higher-order forecasts or responses are considered, due to parameter Model misspecification in multivariate econometric models can strongly influence estimates of quantities of interest such as structural parameters, forecast distributions or responses to structural shocks, even more so if higher-order forecasts or responses are considered, due to parameter convolution. We propose a simple method for addressing these specification issues in the context of Bayesian VARs. Our method, called coarsened Bayesian VARs (cBVARs), replaces the exact likelihood with a coarsened likelihood that takes into account that the model might be misspecified along important but unknown dimensions. Since endogenous variables in a VAR can feature different degrees of misspecification, our model allows for this and automatically detects the degree of misspecification. The resulting cBVARs perform well in simulations for several types of misspecification. Applied to US data, cBVARs improve point and density forecasts compared to standard BVARs.

econ.EM↗

arXiv2025

MassSpecGym: A benchmark for the discovery and identification of molecules

The discovery and identification of molecules in biological and environmental samples is crucial for advancing biomedical and chemical sciences. Tandem mass spectrometry (MS/MS) is the leading technique for high-throughput elucidation of molecular structures. However, decoding a molecular structure from its mass spectrum is exceptionally challenging, even when performed by human experts. As a result, the vast majority of acquired MS/MS spectra remain uninterpreted, thereby limiting our understanding of the underlying (bio)chemical processes. Despite decades of progress in machine learning applications for predicting molecular structures from MS/MS spectra, the development of new methods is severely hindered by the lack of standard datasets and evaluation protocols. To address this problem, we propose MassSpecGym -- the first comprehensive benchmark for the discovery and identification of molecules from MS/MS data. Our benchmark comprises the largest publicly available collection of high-quality labeled MS/MS spectra and defines three MS/MS annotation challenges: de novo molecular structure generation, molecule retrieval, and spectrum simulation. It includes new evaluation metrics and a generalization-demanding data split, therefore standardizing the MS/MS annotation tasks and rendering the problem accessible to the broad machine learning community. MassSpecGym is publicly available at https://github.com/pluskal-lab/MassSpecGym.

q-bio.QM↗

arXiv2025

Global martingale solutions for stochastic Shigesada-Kawasaki-Teramoto population models

The existence of global nonnegative martingale solutions to cross-diffusion systems of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven. The model describes the stochastic segregation dynamics of an arbitrary number of population species in a bounded domain with no-flux boundary conditions. The diffusion matrix is generally neither symmetric nor positive semidefinite, which excludes standard methods for evolution equations. Instead, the existence proof is based on the entropy structure of the model, a novel regularization of the entropy variable, higher-order moment estimates, and fractional time regularity. The regularization technique is generic and is applied to the population system with self-diffusion in any space dimension and without self-diffusion in two space dimensions.

math.PR↗

arXiv2024

Experimental Demonstration of Logical Magic State Distillation

Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and corrected, enabling substantial reduction in logical error rates. However, the set of logical operations that can be easily implemented on such encoded qubits is often constrained, necessitating the use of special resource states known as 'magic states' to implement universal, classically hard circuits. A key method to prepare high-fidelity magic states is to perform 'distillation', creating them from multiple lower fidelity inputs. Here we present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer. Our approach makes use of a dynamically reconfigurable architecture to encode and perform quantum operations on many logical qubits in parallel. We demonstrate the distillation of magic states encoded in d=3 and d=5 color codes, observing improvements of the logical fidelity of the output magic states compared to the input logical magic states. These experiments demonstrate a key building block of universal fault-tolerant quantum computation, and represent an important step towards large-scale logical quantum processors.

quant-ph↗

arXiv2024

Machine Learning the Macroeconomic Effects of Financial Shocks

We propose a method to learn the nonlinear impulse responses to structural shocks using neural networks, and apply it to uncover the effects of US financial shocks. The results reveal substantial asymmetries with respect to the sign of the shock. Adverse financial shocks have powerful effects on the US economy, while benign shocks trigger much smaller reactions. Instead, with respect to the size of the shocks, we find no discernible asymmetries.

econ.EM↗

arXiv2024

The Distributional Effects of Economic Uncertainty

We study the distributional implications of uncertainty shocks by developing a model that links macroeconomic aggregates to the US distribution of earnings and consumption. We find that: initially, the fraction of low-earning workers decreases, while the share of households reporting low consumption increases; at longer horizons, the fraction of low-income workers increases, but the consumption distribution reverts to its pre-shock shape. While the first phase reduces income inequality and increases consumption inequality, in the second stage income inequality rises, while the effects on consumption inequality dissipate. Finally, we introduce Functional Local Projections and show that they yield similar results.

econ.GN↗