Simin Shekarpaz

Simin Shekarpaz, Mohammad Azizmalayeri, Mohammad Hossein Rohban

In this paper, we propose the physics informed adversarial training (PIAT) of neural networks for solving nonlinear differential equations (NDE). It is well-known that the standard training of neural networks results in non-smooth functions. Adversarial training (AT) is an established defense mechanism against adversarial attacks, which could also help in making the solution smooth. AT include augmenting the training mini-batch with a perturbation that makes the network output mismatch the desired output adversarially. Unlike formal AT, which relies only on the training data, here we encode the governing physical laws in the form of nonlinear differential equations using automatic differentiation in the adversarial network architecture. We compare PIAT with PINN to indicate the effectiveness of our method in solving NDEs for up to 10 dimensions. Moreover, we propose weight decay and Gaussian smoothing to demonstrate the PIAT advantages. The code repository is available at https://github.com/rohban-lab/PIAT.

Simin Shekarpaz, Fanhai Zeng, George Karniadakis

We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the challenge of applying PINNs to forward dynamical systems and demonstrates improved accuracy through its application to neuron models. Specifically, we apply operator splitting to decompose the original neuron model into sub-problems that are then solved using PINNs. Moreover, we develop an $L^1$ scheme for discretizing fractional derivatives in fractional neuron models, leading to improved accuracy and efficiency. The results of this study highlight the potential of splitting PINNs in solving both integer- and fractional-order neuron models, as well as other similar systems in computational science and engineering.

Yilan Qin, Chuanfei Dong, Hongyang Zhou et al.

The plasma environment around Mars is highly variable because it is strongly influenced by the solar wind. Accurate identification of plasma regions around Mars is important for the community studying solar wind-Mars interactions, region-specific plasma processes, and atmospheric escape. In this study, we develop a machine-learning-based classifier to automatically identify three key plasma regions--solar wind, magnetosheath, and induced magnetosphere--using only ion omnidirectional energy spectra measured by the MAVEN Solar Wind Ion Analyzer (SWIA). Two neural network architectures are evaluated: a multilayer perceptron (MLP) and a convolutional neural network (CNN) that incorporates short temporal sequences. Our results show that the CNN can reliably distinguish the three plasma regions, whereas the MLP struggles to separate the solar wind and magnetosheath. Therefore, the CNN-based approach provides an efficient and accurate framework for large-scale plasma region identification at Mars and can be readily applied to future planetary missions.

Jiawei Gao, Chuanfei Dong, Chi Zhang et al.

Understanding the magnetic field environment around Mars and its response to upstream solar wind conditions provide key insights into the processes driving atmospheric ion escape. To date, global models of Martian induced magnetosphere have been exclusively physics-based, relying on computationally intensive simulations. For the first time, we develop a data-driven model of the Martian induced magnetospheric magnetic field using Physics-Informed Neural Network (PINN) combined with MAVEN observations and physical laws. Trained under varying solar wind conditions, including B_IMF, P_SW, and θ_cone, the data-driven model accurately reconstructs the three-dimensional magnetic field configuration and its variability in response to upstream solar wind drivers. Based on the PINN results, we identify key dependencies of magnetic field configuration on solar wind parameters, including the hemispheric asymmetries of the draped field line strength in the Mars-Solar-Electric coordinates. These findings demonstrate the capability of PINNs to reconstruct complex magnetic field structures in the Martian induced magnetosphere, thereby offering a promising tool for advancing studies of solar wind-Mars interactions.