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I present a simple hybrid framework that combines physics informed neural networks (PINNs) with features generated from small quantum circuits. As a proof of concept, a first-order equation is solved by feeding quantum measurement…
Neural network models have shown outstanding performance and successful resolutions to complex problems in various fields. However, the majority of these models are viewed as black-box, requiring a significant amount of data for…
Differential equations are involved in modeling many engineering problems. Many efforts have been devoted to solving differential equations. Due to the flexibility of neural networks, Physics Informed Neural Networks (PINNs) have recently…
Domain generalization in image classification is a crucial challenge, with models often failing to generalize well across unseen datasets. We address this issue by introducing a neuro-inspired Neural Response Normalization (NeuRN) layer…
The complex and unique neural network topology of the human brain formed through natural evolution enables it to perform multiple cognitive functions simultaneously. Automated evolutionary mechanisms of biological network structure inspire…
The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…
We put forth two physics-informed neural network (PINN) schemes based on Miura transformations and the novelty of this research is the incorporation of Miura transformation constraints into neural networks to solve nonlinear PDEs. The most…
Accurate grain orientation mapping is essential for understanding and optimizing the performance of polycrystalline materials, particularly in energy-related applications. Lithium nickel oxide (LiNiO$_{2}$) is a promising cathode material…
In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful…
Neural networks (NNs) accelerate simulations of quantum dissipative dynamics. Ensuring that these simulations adhere to fundamental physical laws is crucial, but has been largely ignored in the state-of-the-art NN approaches. We show that…
Physics-Informed Neural Networks (PINNs) are a useful framework for approximating partial differential equation solutions using deep learning methods. In this paper, we propose a principled redesign of the PINNsformer, a Transformer-based…
Physics-informed neural network (PINN) has been a prevalent framework for solving PDEs since proposed. By incorporating the physical information into the neural network through loss functions, it can predict solutions to PDEs in an…
We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations…
Neural networks, while powerful, often lack interpretability. Physics-Informed Neural Networks (PINNs) address this limitation by incorporating physics laws into the loss function, making them applicable to solving Ordinary Differential…
This work proposes a novel approach to the deep hierarchical classification task, i.e., the problem of classifying data according to multiple labels organized in a rigid parent-child structure. It consists in a multi-output deep neural…
Recently, Deep-Neural-Network (DNN) based edge prediction is progressing fast. Although the DNN based schemes outperform the traditional edge detectors, they have much higher computational complexity. It could be that the DNN based edge…
Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures…
Hypergraph neural networks can model multi-way connections among nodes of the graphs, which are common in real-world applications such as genetic medicine. In particular, genetic pathways or gene sets encode molecular functions driven by…
Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…
We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiative tranfer equations.…