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Change point detection (CPD) and anomaly detection (AD) are essential techniques in various fields to identify abrupt changes or abnormal data instances. However, existing methods are often constrained to univariate data, face scalability…

Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers…

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…

Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…

EODECA (Engineered Ordinary Differential Equations as Classification Algorithm) is a novel approach at the intersection of machine learning and dynamical systems theory, presenting a unique framework for classification tasks [1]. This…

The neural ordinary differential equation (neural ODE) model has attracted increasing attention in time series analysis for its capability to process irregular time steps, i.e., data are not observed over equally-spaced time intervals. In…

A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such…

In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE),…

Colloids have a striking relevance in a wide spectrum of industrial formulations, spanning from personal care products to protective paints. Their behaviour can be easily influenced by extremely weak forces, which disturb their…

The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…

Differential computation (DC) is a highly general incremental computation/view maintenance technique that can maintain the output of an arbitrary and possibly recursive dataflow computation upon changes to its base inputs. As such, it is a…

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…

The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…

Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…

Joint clustering and feature learning methods have shown remarkable performance in unsupervised representation learning. However, the training schedule alternating between feature clustering and network parameters update leads to unstable…

Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…