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Deep learning algorithms excel at extracting patterns from raw data, and with large datasets, they have been very successful in computer vision and natural language applications. However, in other domains, large datasets on which to learn…

We present a new dependent type system, NM-DEKL$^3_\infty$ (Non-Monotone Dependent Knowledge-Enhanced Logic), for formalising evolving knowledge in dynamic environments. The system uses a three-layer architecture separating a computational…

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here…

We demonstrate how deep convolutional neural networks can be trained to predict 2+1 D hydrodynamic simulation results for flow coefficients, mean-transverse-momentum and charged particle multiplicity from the initial energy density profile.…

Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…

We present a data-driven framework for turbulence modeling, applied to flow prediction in the FDA nozzle. In this study, the standard RANS equations have been modified using an implicit-explicit hybrid approach. New variables were…

Deep learning method has attracted tremendous attention to handle fluid dynamics in recent years. However, the deep learning method requires much data to guarantee the generalization ability and the data of fluid dynamics are deficient.…

Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point…

Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional…

Researchers have been highly active to investigate the classical machine learning workflow and integrate best practices from the software engineering lifecycle. However, deep learning exhibits deviations that are not yet covered in this…

We introduce a general framework for constructing coarse-grained potential models without ad hoc approximations such as limiting the potential to two- and/or three-body contributions. The scheme, called Deep Coarse-Grained Potential…

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

In the field of fluid numerical analysis, there has been a long-standing problem: lacking of a rigorous mathematical tool to map from a continuous flow field to discrete vortex particles, hurdling the Lagrangian particles from inheriting…

Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However,…