Related papers: Universal Differential Equations for Scientific Ma…

Discrete event simulation specification (DEVS) is a formalism designed to describe both discrete state and continuous state systems. It is a powerful abstract mathematical notation. However, until recently it lacked proper graphical…

Species distribution models (SDMs) aim to predict the distribution of species by relating occurrence data with environmental variables. Recent applications of deep learning to SDMs have enabled new avenues, specifically the inclusion of…

Recently, symbolic computation and computer algebra systems have been successfully applied in systems biology, especially in chemical reaction network theory. One advantage of symbolic computation is its potential for qualitative answers to…

Ecosystems are governed by dynamic processes such as competition for resources, reproduction and dispersal. These shape their biodiversity and how the system responds to change. Current approaches to modelling ecosystems, especially plants,…

Universal image representations are critical in enabling real-world fine-grained and instance-level recognition applications, where objects and entities from any domain must be identified at large scale. Despite recent advances, existing…

Differentiable programming is the combination of classical neural networks modules with algorithmic ones in an end-to-end differentiable model. These new models, that use automatic differentiation to calculate gradients, have new learning…

Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations…

This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…

Multimodal learning, integrating histology images and genomics, promises to enhance precision oncology with comprehensive views at microscopic and molecular levels. However, existing methods may not sufficiently model the shared or…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

Performant numerical solving of differential equations is required for large-scale scientific modeling. In this manuscript we focus on two questions: (1) how can researchers empirically verify theoretical advances and consistently compare…

The UDC (Universal Decimal Classification) is not only a classification language with a long history; it also presents a complex cognitive system worthy of the attention of complexity theory. The elements of the UDC: classes, auxiliaries,…

We are delighted to see the recent development of physics-informed extreme learning machine (PIELM) for its higher computational efficiency and accuracy compared to other physics-informed machine learning (PIML) paradigms. Since a…

Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…

Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…

The ability to estimate epistemic uncertainty is often crucial when deploying machine learning in the real world, but modern methods often produce overconfident, uncalibrated uncertainty predictions. A common approach to quantify epistemic…

Continuous dynamical systems, characterized by differential equations, are ubiquitously used to model several important problems: plasma dynamics, flow through porous media, weather forecasting, and epidemic dynamics. Recently, a wide range…

Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex…

Visual data is used in numerous different scientific workflows ranging from remote sensing to ecology. As the amount of observation data increases, the challenge is not just to make accurate predictions but also to understand the underlying…