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We propose a novel method for closed-form predictive distribution modeling with neural nets. In quantifying prediction uncertainty, we build on Evidential Deep Learning, which has been impactful as being both simple to implement and giving…

Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…

To improve the predictive capacity of system models in the input-output sense, this paper presents a framework for model updating via learning of modeling uncertainties in locally (and thus also in globally) Lipschitz nonlinear systems.…

This paper aims to provide a practical example on the assessment and propagation of input uncertainty for option pricing when using tree-based methods. Input uncertainty is propagated into output uncertainty, reflecting that option prices…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

In this paper, we introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually…

We show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in Physics for a variety of quantum thermodynamics applications, can be used to develop an…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…

Computational color constancy refers to the estimation of the scene illumination and makes the perceived color relatively stable under varying illumination. In the past few years, deep Convolutional Neural Networks (CNNs) have delivered…

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention…

Uncertainty estimation in machine learning is paramount for enhancing the reliability and interpretability of predictive models, especially in high-stakes real-world scenarios. Despite the availability of numerous methods, they often pose a…

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

This paper introduces a novel optimization-based approach for parametric nonlinear system identification. Building upon the prediction error method framework, traditionally used for linear system identification, we extend its capabilities…

This paper presents a novel way to predict options price for one day in advance, utilizing the method of Quasi-Reversibility for solving the Black-Scholes equation. The Black-Scholes equation solved forwards in time with Tikhonov…

The identification of black-box nonlinear state-space models requires a flexible representation of the state and output equation. Artificial neural networks have proven to provide such a representation. However, as in many identification…

The principal portfolio approach is an emerging method in signal-based trading. However, these principal portfolios may not be diversified to explore the key features of the prediction matrix or robust to different situations. To address…