DiffGrad for Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) are regarded as state-of-the-art tools for addressing highly nonlinear problems based on partial differential equations. Despite their broad range of applications, PINNs encounter several performance challenges, including issues related to efficiency, minimization of computational cost, and enhancement of accuracy. Burgers' equation, a fundamental equation in fluid dynamics that is extensively used in PINNs, provides flexible results with the Adam optimizer that does not account for past gradients. This paper introduces a novel strategy for solving Burgers' equation by incorporating DiffGrad with PINNs, a method that leverages the difference between current and immediately preceding gradients to enhance performance. A comprehensive computational analysis is conducted using optimizers such as Adam, Adamax, RMSprop, and DiffGrad to evaluate and compare their effectiveness. Our approach includes visualizing the solutions over space at various time intervals to demonstrate the accuracy of the network. The results show that DiffGrad not only improves the accuracy of the solution but also reduces training time compared to the other optimizers.

SwishReLU: A Unified Approach to Activation Functions for Enhanced Deep Neural Networks Performance

ReLU, a commonly used activation function in deep neural networks, is prone to the issue of "Dying ReLU". Several enhanced versions, such as ELU, SeLU, and Swish, have been introduced and are considered to be less commonly utilized. However, replacing ReLU can be somewhat challenging due to its inconsistent advantages. While Swish offers a smoother transition similar to ReLU, its utilization generally incurs a greater computational burden compared to ReLU. This paper proposes SwishReLU, a novel activation function combining elements of ReLU and Swish. Our findings reveal that SwishReLU outperforms ReLU in performance with a lower computational cost than Swish. This paper undertakes an examination and comparison of different types of ReLU variants with SwishReLU. Specifically, we compare ELU and SeLU along with Tanh on three datasets: CIFAR-10, CIFAR-100 and MNIST. Notably, applying SwishReLU in the VGG16 model described in Algorithm 2 yields a 6% accuracy improvement on the CIFAR-10 dataset.

ASU-CNN: An Efficient Deep Architecture for Image Classification and Feature Visualizations

Activation functions play a decisive role in determining the capacity of Deep Neural Networks as they enable neural networks to capture inherent nonlinearities present in data fed to them. The prior research on activation functions primarily focused on the utility of monotonic or non-oscillatory functions, until Growing Cosine Unit broke the taboo for a number of applications. In this paper, a Convolutional Neural Network model named as ASU-CNN is proposed which utilizes recently designed activation function ASU across its layers. The effect of this non-monotonic and oscillatory function is inspected through feature map visualizations from different convolutional layers. The optimization of proposed network is offered by Adam with a fine-tuned adjustment of learning rate. The network achieved promising results on both training and testing data for the classification of CIFAR-10. The experimental results affirm the computational feasibility and efficacy of the proposed model for performing tasks related to the field of computer vision.

Amplifying Sine Unit: An Oscillatory Activation Function for Deep Neural Networks to Recover Nonlinear Oscillations Efficiently

Many industrial and real life problems exhibit highly nonlinear periodic behaviors and the conventional methods may fall short of finding their analytical or closed form solutions. Such problems demand some cutting edge computational tools with increased functionality and reduced cost. Recently, deep neural networks have gained massive research interest due to their ability to handle large data and universality to learn complex functions. In this work, we put forward a methodology based on deep neural networks with responsive layers structure to deal nonlinear oscillations in microelectromechanical systems. We incorporated some oscillatory and non oscillatory activation functions such as growing cosine unit known as GCU, Sine, Mish and Tanh in our designed network to have a comprehensive analysis on their performance for highly nonlinear and vibrational problems. Integrating oscillatory activation functions with deep neural networks definitely outperform in predicting the periodic patterns of underlying systems. To support oscillatory actuation for nonlinear systems, we have proposed a novel oscillatory activation function called Amplifying Sine Unit denoted as ASU which is more efficient than GCU for complex vibratory systems such as microelectromechanical systems. Experimental results show that the designed network with our proposed activation function ASU is more reliable and robust to handle the challenges posed by nonlinearity and oscillations. To validate the proposed methodology, outputs of our networks are being compared with the results from Livermore solver for ordinary differential equation called LSODA. Further, graphical illustrations of incurred errors are also being presented in the work.