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In deep multi-task learning, weights of task-specific networks are shared between tasks to improve performance on each single one. Since the question, which weights to share between layers, is difficult to answer, human-designed…
A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…
Recent advances in deep learning have pushed the performances of visual saliency models way further than it has ever been. Numerous models in the literature present new ways to design neural networks, to arrange gaze pattern data, or to…
Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…
Dynamic optimisation occurs in a variety of real-world problems. To tackle these problems, evolutionary algorithms have been extensively used due to their effectiveness and minimum design effort. However, for dynamic problems, extra…
The purpose of this study is to utilize the Chebyshev spectral method neural network(CSNN) model to solve differential equations. This approach employs a single-layer neural network wherein Chebyshev spectral methods are used to construct…
We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
Numerical modelling is an essential approach to understanding the behavior of thermal plasmas in various industrial applications. We propose a deep learning method for solving the partial differential equations in thermal plasma models. In…
The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific…
Physics-Informed Neural Networks (PINNs) have emerged as a promising machine learning approach for solving partial differential equations (PDEs). However, PINNs face significant challenges in balancing multi-objective losses, as multiple…
This short note describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. DNNs are being widely used to predict phenomena in physics and mechanics. One of the issues of DNNs is that…
Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…
Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…
Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…
In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…