With the vigorous development of AI for Science in recent years, the integration of artificial intelligence and various scientific disciplines has become a major trend. However, AI for Science covers a wide range and involves many disciplines. Therefore, organizing it into a unified framework will enable better navigation for newcomers to the field. In this article, we posit that although the objects and methods of scientific research seem to be vastly different, AI can provide a universal paradigm and methods for scientific research in the following three aspects: scientific simulation, design and control, and discovery, solving problems in the field. This article will specifically elaborate on the task setting and current representative work. Through specific examples, we will explain how AI can concretely assist scientific research, facilitating researchers to better apply existing methods or develop novel methods.

Physics-Informed Neural Networks (PINN) have provided a new way of numerically solving forward and inverse problems of partial differential equations with promising applications. This paper focuses on the diffusion coefficient inverse problem of the diffusion equation. A systematic study is carried out for the problems of fixed coefficients, anisotropic coefficients, spatial dependence coefficients, spatio-temporal dependence coefficients, and nonlinear diffusion coefficients, and the neural network structure and solution method required for solving each type of problem are proposed. Numerical experiments show that the PINN method can reconstruct the unknown coefficients accurately with less data and is robust under a certain noise level.

The residual neural network is used to carry out machine learning on the steady-state flow field of the hemisphere-on-cylinder laser turret model in the range of Ma=0.3~0.8, and the subsonic/transonic flow field under any incoming flow conditions in this range is established. The prediction accuracy of this model is evaluated for beam wavefront distortion under different view-of-field angles. The learning model reproduces flow characteristics such as boundary layers, flow separation, and separated shear layers in turret flows, including in particular unanchored shock discontinuities in transonic flow. The wavefront distribution based on the predicted flow field under different viewing angles is basically consistent with that calculated based on the flow field of CFD. This machine learning method provides a strategy for adaptive correction of laser turret aero-optical effects in the engineering field.

The gas kinetic scheme based on Cahn-Hilliard phase field equation with interfacial fluxes determined by the Chapman-Enskog first-order approximation is constructed in the framework of finite volume. It is further demonstrated that the proposed model can be accurately recovered to Cahn-Hilliard equation. The method is tested through several cases and compared with the corresponding lattice Boltzmann method. The results show that the method in this paper has excellent accuracy and numerical stability for interface trapping. The study extends application of the gas-kinetic scheme to phase-field theory and provides a new solution for the simulation of two-phase fluid systems.

Based on the lubrication theory and the coupling between gas phase diffusion and droplet evaporation, a mathematical model of droplet evaporation on a solid substrate with uniform wall temperature is established, and the evolution equation of droplet thickness based on the gas phase diffusion model is derived. The quasi-static gas phase field is solved with the droplet contact line dynamics, and the influence of Ma and Pe_k on the droplet evaporation under the effect of gas phase is discussed through numerical simulation. The results show that under the same parameters, the droplet evaporation process of the gas phase diffusion model is slower than that of the one-sided model, and the contact radius and the evaporating rate is decreased, and the results are more consistent with the experimental results. Under the gas phase diffusion model, the droplet evaporating rate is increased and the droplet evaporation process is shortened by reducing Ma, thereby promoting droplet evaporation. By increasing Pe_k, the gas density near the droplet is densified, and the droplet evaporation is enhanced.

In order to quantitatively evaluate water blocking damage of tight reservoirs in flowback period, based on the relationship between capillary pressure and relative permeability with water saturation, Darcy's formula was used to characterize gas-water two-phase flow equations in invaded areas, and a quantitative evaluation model of water blocking damage of fracturing fluid in tight reservoir was established. The water saturation, relative permeability and permeability damage degree of invaded areas in flowback period were solved by the Taylor's nonlinear solution method, and the effect of fracturing fluid invasion depth, fracturing fluid viscosity, flowback and production differential pressure and pressure sensitivity were analyzed. The results show that, water blocking damage starts to gradually be relieved once the pressure differential of flowback and production exceeds the capillary force. The higher the differential pressure between flowback and production, the more effectively water blockage can be relieved and the less damage water blockage can cause. It is challenging to release the water blockage at the flowback period when the invasion depth, viscosity, and stress sensitivity coefficient of the fracturing fluid are high. The higher the damage degree of the water blockage, the lower the recovery of gas will finally be.

Based on second-order time discretization of BDF2, this paper presents a simpler approach for designing algorithms for coupling radiation, ion and electron energies via operator splitting method. Numerical results show the error and computational cost of iterative operator splitting method is less than that of operator splitting method with the same time discretization order, and while compared with first-order backward Euler method, time steps of second-order BDF2 can be ten times lager for obtaining the same computational accuracy. This new proposed second-order time discretization iterative operator splitting method can be used for simulating ICF physical models, and promoting the computational efficiency.

In the fields of ocean engineering and aerospace, the motion state of fluids has a significant impact on the performance and stability of systems. Stokes equations with damping terms are commonly used to describe the flow behavior of fluids under damping, such as the fluids in porous media. Two numerical iterative algorithms based on finite element discretization are proposed for the steady incompressible Stokes questions with the nonlinear damping term. The basic idea is to first use the finite element method to solve the Stokes problem and obtain the initial iterative solution. Secondly, it uses the Stokes iterative algorithm or Oseen iterative algorithm to solve the steady incompressible Stokes problem with nonlinear damping term and obtain approximate finite element solutions. Convergence and stability of the proposed algorithms are analyzed. Error estimates of the obtained approximate solutions are derived. Some numerical results are also given to show correctness of theoretical analysis and effectiveness of the algorithms. The results show that when the equation satisfies the stability condition, both numerical iterative algorithms are feasible.

Highly enriched uranium subcritical assemblies with and without low atomic number (low-Z) reflectors are modeled. The neutron and photon transport process in the assemblies initiated by a pulsed neutron source is simulated using the Monte Carlo code. When the size or mass density of the fissile region and the reflector changes, the effective multiplication factor k_eff of the fissile region or the whole system changes accordingly (for assemblies without reflectors, the fissile region refers to the whole system). For each case, the time dependence of leakage γ count rate, neutron population in the fissile region and their ratio is obtained and analyzed to investigate the applicability and limitation of the pulsed neutron source (PNS) method for subcritical systems with and without reflectors. It is indicated that the PNS method is suitable for systems of which the fissile region is near-critical, i.e., the k_eff value of the fissile region is close to 1. The closer the fissile region is to the critical state, the more accurately the leakage γ count rate can reflect the fissile region's fission decay properties during the specific time window. For the highly enriched uranium assemblies described in this paper, the k_eff threshold of the fissile region ensuring the applicability of the PNS method is given. In addition, the possibility of applying the PNS method under dynamic conditions are also discussed according to the calculation results.

Memristor coupled neurons have complex nonlinear dynamic behavior and have been widely used in neural computing and chaotic systems. In this paper, a new magnetic controlled memristor model is proposed, and the Hindmarsh-Rose(HR) neuron model is established. The neural model is analyzed by bifurcating diagram, Lyapunov exponent spectrum, phase diagram and time series diagram. Then the chaotic sequence generated by the model is applied to the DNA chaotic image encryption algorithm. The experimental results show that this HR neuron model can generate multiple discharge modes and complex chaotic behavior under the influence of magnetic induction intensity, and the generated chaotic sequences based on the model have the characteristics of randomness, initial value sensitivity, ergodic, etc., which has strong security when applied to chaotic image encryption algorithms. These results will provide strong support for understanding the dynamics of neuron hiding and constructing memristor neural network, and have great application value for the treatment of neuron-related lesions.

The electromagnetic environment around neurons is very complex, and it is important to study the effect of electromagnetic radiation on neuronal behavior. Electromagnetic radiation is simulated by the induced current of a magnetically controlled memristor to study the behavior of tangent-type memristor-coupled Hindmarsh-Rose (HR) neural network dynamics in a small world of NW under the effect of electromagnetic radiation. Numerical simulations have found that increasing the coupling strength promotes synchronization between neurons and alters their firing pattern; the neural network is sensitive to the initial value when the electromagnetic radiation effect is in effect, and it is also found that electromagnetic radiation enhances the energy required for neuronal firing by Hamiltonian energy. When amnesic coupling and electromagnetic radiation effect act together, the smaller the intensity of electromagnetic radiation, the more effective amnesic coupling can promote network synchronization. The experimental results show that the tangent-type amnesia-coupled neural network under the effect of electromagnetic radiation is sensitive to the state of the initial value, and the synchronization behavior and discharge activity of the neural network are related to the coupling strength and electromagnetic radiation.