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Researcher profile

Daniele Venturi

Daniele Venturi contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.NANumerical AnalysisMachine Learningphysics.comp-phmath-phmath.MPComputational Engineering, Finance, and ScienceCryptography and Securityeess.SYphysics.chem-ph

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Published work

9 published item(s)

preprint2026arXiv

Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins

Digital twins (DTs) rely on continuous synchronization between physical systems and their virtual counterparts through online parameter estimation under uncertainty. In many practical settings, however, this task is challenged by low observability, weak excitation, nonlinear dynamics, and noisy or biased measurements. In this work, we develop a new mathematical framework that integrates Weighted Flow Matching (WFM) generative modeling with physics-informed nonlinear filtering to enhance parameter estimation in DTs. WFM relies on dynamic reweighting of training samples, which guides the generative model toward parameter regimes most informative of the evolving system state. This generative component is tightly coupled with a physics-informed filtering architecture based on the Unscented Kalman Filter (UKF), yielding a unified DT framework that combines data-driven probability transport with physically consistent state and parameter estimation. The effectiveness of the new integrated framework is demonstrated within a spacecraft DT architecture, where stable moment of inertia estimation is achieved under uncertain and noisy sensing, with significant performance improvements over established approaches such as Extended Kalman Filtering (EKF) and Ensemble Kalman Filtering (EnKF). These results highlight the potential of weighted generative modeling as a core mechanism for real-time DT synchronization in operational and mission-critical systems.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Generative forecasting with joint probability models

Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by learning distributions over plausible system evolutions; yet, most existing approaches focus on next-step conditional prediction rather than the structure of the underlying dynamics. In this work, we reframe forecasting as a fully generative problem by learning the joint probability distribution of lagged system states over short temporal windows and obtaining forecasts through marginalization. This new perspective allows the model to capture nonlinear temporal dependencies, represent multistep trajectory segments, and produce next-step predictions consistent with the learned joint distribution. We also introduce a general, model-agnostic training and inference framework for joint generative forecasting and show how it enables assessment of forecast robustness and reliability using three complementary uncertainty quantification metrics (ensemble variance, short-horizon autocorrelation, and cumulative Wasserstein drift), without access to ground truth. We evaluate the performance of the proposed method on two canonical chaotic dynamical systems, the Lorenz-63 system and the Kuramoto-Sivashinsky equation, and show that joint generative models yield improved short-term predictive skill, preserve attractor geometry, and achieve substantially more accurate long-range statistical behaviour than conventional conditional next-step models.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Adaptive integration of nonlinear evolution equations on tensor manifolds

We develop new adaptive algorithms for temporal integration of nonlinear evolution equations on tensor manifolds. These algorithms, which we call step-truncation methods, are based on performing one time step with a conventional time-stepping scheme, followed by a truncation operation onto a tensor manifold. By selecting the rank of the tensor manifold adaptively to satisfy stability and accuracy requirements, we prove convergence of a wide range of step-truncation methods, including explicit one-step and multi-step methods. These methods are very easy to implement as they rely only on arithmetic operations between tensors, which can be performed by efficient and scalable parallel algorithms. Adaptive step-truncation methods can be used to compute numerical solutions of high-dimensional PDEs, which have become central to many new areas of application such optimal mass transport, random dynamical systems, and mean field optimal control. Numerical applications are presented and discussed for a Fokker-Planck equation with spatially dependent drift on a flat torus of dimension two and four.

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preprint2022arXiv

Cryptographic and Financial Fairness

A recent trend in multi-party computation is to achieve cryptographic fairness via monetary penalties, i.e. each honest player either obtains the output or receives a compensation in the form of a cryptocurrency. We pioneer another type of fairness, financial fairness, that is closer to the real-world valuation of financial transactions. Intuitively, a penalty protocol is financially fair if the net present cost of participation (the total value of cash inflows less cash outflows, weighted by the relative discount rate) is the same for all honest participants, even when some parties cheat. We formally define the notion, show several impossibility results based on game theory, and analyze the practical effects of (lack of) financial fairness if one was to run the protocols for real on Bitcoin using Bloomberg's dark pool trading. For example, we show that the ladder protocol (CRYPTO'14), and its variants (CCS'15 and CCS'16), fail to achieve financial fairness both in theory and in practice, while the penalty protocols of Kumaresan and Bentov (CCS'14) and Baum, David and Dowsley (FC'20) are financially fair. This version contains formal definitions, detailed security proofs, demos and experimental data in the appendix.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Improving neural network predictions of material properties with limited data using transfer learning

We develop new transfer learning algorithms to accelerate prediction of material properties from ab initio simulations based on density functional theory (DFT). Transfer learning has been successfully utilized for data-efficient modeling in applications other than materials science, and it allows transferable representations learned from large datasets to be repurposed for learning new tasks even with small datasets. In the context of materials science, this opens the possibility to develop generalizable neural network models that can be repurposed on other materials, without the need of generating a large (computationally expensive) training set of materials properties. The proposed transfer learning algorithms are demonstrated on predicting the Gibbs free energy of light transition metal oxides.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

A new scalable algorithm for computational optimal control under uncertainty

We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random parameters or processes. The objective is to provide a validated new computational capability for optimal control which will be achieved more efficiently than current state-of-the-art methods. The new framework utilizes direct single or multi-shooting discretization, and is based on efficient vectorized gradient computation with adaptable memory management. The algorithm is demonstrated to be scalable to high-dimensional nonlinear control systems with random initial condition and unknown parameters.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Dynamically orthogonal tensor methods for high-dimensional nonlinear PDEs

We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical decomposition of the approximation space obtained by splitting the independent variables of the problem into disjoint subsets. This process, which can be conveniently be visualized in terms of binary trees, yields series expansions analogous to the classical Tensor-Train and Hierarchical Tucker tensor formats. By enforcing dynamic orthogonality conditions at each level of binary tree, we obtain coupled evolution equations for the modes spanning each subspace within the hierarchical decomposition. This allows us to effectively compute the solution to high-dimensional time-dependent nonlinear PDEs on tensor manifolds of constant rank, with no need for rank reduction methods. We also propose new algorithms for dynamic addition and removal of modes within each subspace. Numerical examples are presented and discussed for high-dimensional hyperbolic and parabolic PDEs in bounded domains.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Generalized Langevin equations for systems with local interactions

We present a new method to approximate the Mori-Zwanzig (MZ) memory integral in generalized Langevin equations (GLEs) describing the evolution of smooth observables in high-dimensional nonlinear systems with local interactions. Building upon the Faber operator series we recently developed for the orthogonal dynamics propagator, and an exact combinatorial algorithm that allows us to compute memory kernels from first principles, we demonstrate that the proposed method is effective in computing auto-correlation functions, intermediate scattering functions and other important statistical properties of the observable. We also develop a new stochastic process representation of the MZ fluctuation term for systems in statistical equilibrium. Numerical applications are presented for the Fermi-Pasta-Ulam model, and for random wave propagation in homogeneous media.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Stability analysis of hierarchical tensor methods for time-dependent PDEs

In this paper we address the question of whether it is possible to integrate time-dependent high-dimensional PDEs with hierarchical tensor methods and explicit time stepping schemes. To this end, we develop sufficient conditions for stability and convergence of tensor solutions evolving on tensor manifolds with constant rank. We also argue that the applicability of PDE solvers with explicit time-stepping may be limited by time-step restriction dependent on the dimension of the problem. Numerical applications are presented and discussed for variable coefficients linear hyperbolic and parabolic PDEs.

0 citations0 reviewsNo code linkedOpen access