Simulating electromagnetic (EM) fields can obtain the EM responses of geoelectric models at different times and spaces, which helps to explain the dynamic process of EM wave propagation underground. EM forward modeling is regarded as the engine of inversion. Traditional numerical methods have certain limitations in simulating the EM responses from large-scale geoelectric models. In recent years, the emerging physics-informed neural networks (PINNs) have given new solutions for geophysical EM field simulations. This paper conducts a preliminary exploration using PINN to simulate geophysical frequency domain EM fields. The proposed PINN performs self-supervised training under physical constraints without any data. Once the training is completed, the responses of EM fields at any position in the geoelectric model can be inferred instantly. Compared with the finite-difference solution, the proposed PINN performs the task of geophysical frequency domain EM field simulations well. The proposed PINN is applicable for simulating the EM response of any one-dimensional geoelectric model under any polarization mode at any frequency and any spatial position. This work provides a new scenario for the application of artificial intelligence in geophysical EM exploration.

The fluctuation of iron ore prices is one of the most important factors affecting policy. Therefore, the accurate prediction of iron ore prices has significant value in analysis and judgment regarding future changes in policies. In this study, we propose a correlation analysis to extract eight influencing factors of iron ore prices and introduce multiple linear regression analysis to the prediction. With historical data, we establish a model to forecast iron ore prices from 2020 to 2024. Taking prices in 2018 and 2019 as samples to test the applicability of the model, we obtain an acceptable level of error between the predicted iron ore prices and the actual prices. The prediction model based on multiple linear regression has high prediction accuracy. Iron ore prices will show a relatively stable upward trend over the next five years without the effects of COVID-19.

Magnetotelluric (MT) data inversion aims to recover subsurface resistivity model by minimizing an objective function, typically comprising a data misfit term and a regularization term (e.g., Tikhonov-style regularization). While gradients-based optimization is widely used, it is prone to local minima and highly sensitive to the initial model. In contrast, nonlinear stochastic algorithms explore a broader solution space but are computationally prohibitive for large-scale MT problems.Deep learning (DL) has emerged as a powerful alternative. Unlike purely data-driven methods, physics-driven DL frameworks embed physical laws, such as wave propagation equation and Maxwell’s equation, as constraints, enhancing interpretability and reducing the need for massive datasets. Implicit neural representation (INR) is a novel physics-driven technique that represents physical properties as continuous functions of spatial coordinates. A key advantage of INR is its inherent ‘frequency principle’ (or spectral bias), where the network learns large-scale (low-frequency) structures before fine-tunning high-resolution (high-frequency) details. In MT inversion, this bias acts as an implicit regularization, improving stability without requiring manually tuned penalty terms.In this paper, we propose an INR-based 2D MT inversion algorithm. Synthetic tests on block and layered models demonstrate that the proposed method recovers anomalous boundaries with higher resolution than traditional Occam-based inversions. Finally, application to the COPROD2 field dataset confirms the practical robustness of the approach and its potential for extension to three-dimensional, mesh-free inversions.