Related papers: Probabilistic Inference on Noisy Time Series (PINT…

Time series modelling is essential for solving tasks such as predictive maintenance, quality control and optimisation. Deep learning is widely used for solving such problems. When managing complex manufacturing process with neural networks,…

This paper introduces for the first time, to the best of our knowledge, the Bayesian Physics-Informed Neural Networks for applications in power systems. Bayesian Physics-Informed Neural Networks (BPINNs) combine the advantages of…

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…

Despite the recent trend of developing and applying neural source code models to software engineering tasks, the quality of such models is insufficient for real-world use. This is because there could be noise in the source code corpora used…

White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that,…

We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…

Network-linked data, where multivariate observations are interconnected by a network, are becoming increasingly prevalent in fields such as sociology and biology. These data often exhibit inherent noise and complex relational structures,…

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Natural and social multivariate systems are commonly studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis…

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

Despite extensive research, time series classification and forecasting on noisy data remain highly challenging. The main difficulties lie in finding suitable mathematical concepts to describe time series and effectively separate noise from…

This article presents a new continuous-time modelling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by L\'{e}vy noise -…

Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…

Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…

Inspired by recent findings on the fractal geometry of language, we introduce Recursive INference Scaling (RINS) as a complementary, plug-in recipe for scaling inference time in language and multimodal systems. RINS is a particular form of…

In order to gain a mechanistic understanding of how tinnitus emerges in the brain, we must build biologically plausible computational models that mimic both tinnitus development and perception, and test the tentative models with brain and…

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

Causal inference permits us to discover covert relationships of various variables in time series. However, in most existing works, the variables mentioned above are the dimensions. The causality between dimensions could be cursory, which…