5 results about "Elliptic partial differential equation" patented technology

Computer systems and methods for training a neural network model to model the dynamical behavior of a fluid. The neural network model is trained based on a network configuration and using a training dataset. The neural network is trained for a plurality of layers that exhibit a ramping down of a spatial resolution between layers followed by a ramping up of the spatial resolution between layers. A test dataset is received representing mathematical characteristics of an elliptical partial differential equation describing dynamical aspects of the fluid. The elliptical partial differential equation is numerically solved using the trained neural network model to determine a solution of the elliptical partial differential equation. The dynamical behavior of the fluid is determined based at least in part on the solution of the elliptical partial differential equation. The dynamical behavior of the fluid is stored in a non-transitory computer-readable memory medium.

The invention discloses a method for realizing large-scale fluid motion simulation based on a spiking neural network, and particularly relates to the field of fluid simulation and artificial intelligence, and the method comprises the steps: S1, constructing a spiking neural network model with recursive connection, encoding high-fidelity fluid data into a pulse event, a composite loss function fusing data fitting and fluid control equation physical constraint is adopted for training; s2, the initial state and the boundary condition of the simulation domain are coded into an initial pulse event and a Poisson pulse sequence synchronized with physical quantity changes; s3, inputting the pulse sequence into the trained model, and calculating and outputting the pulse sequence through neuronal dynamics; and S4, mapping the emission rate of the output pulse into a physical quantity space gradient field, and solving the elliptic partial differential equation to reconstruct a complete physical field at the next moment and update the state. According to the method, the event-driven characteristics of the spiking neural network are utilized, and the calculation efficiency of large-scale fluid simulation is remarkably improved while the simulation precision is ensured.

The invention discloses a high-precision calculation method for a partial differential equation with an interface based on an immersed interface technology, and relates to the field of partial differential equation numerical solutions. According to the method, aiming at an elliptic partial differential equation containing an interface, a homogeneous function is constructed through a potential theory to realize homogeneous processing of an interface jump condition, numerical discretization is carried out in combination with a stable generalized finite element method (SGFEM), and high-precision solution is realized on a non-body-fitted grid by utilizing a boundary integral equation fast algorithm and a singular integral processing technology. The method does not need to depend on a body-fitted grid, reduces the grid division complexity, improves the calculation efficiency and precision, and is suitable for two-dimensional and three-dimensional complex interface problems.

The invention provides an incompressible fluid elliptic partial differential equation wavelet transform convolutional neural network multi-network (WTCNN-MG) numerical solution method, and belongs to the field of incompressible fluid mechanics numerical calculation, and the method specifically comprises the steps: adaptively optimizing convolution-based smoothing, differential, limiting and continuation operations, and reducing the spectral radius of an iteration matrix; the WTCNN is integrated to carry out additional self-adaptive low-frequency smoothing error correction on the coarse grid hierarchy; and low-frequency and high-frequency characteristics are effectively extracted by using the multi-resolution characteristic of the wavelet, and rapid approximation of a low-frequency smoothing error is realized. The invention designs an integrally differentiable WTCNN-MG method, on the premise of ensuring the same precision as the MG method, the calculation efficiency is improved by nearly 90 times, and an efficient incompressible fluid elliptic partial differential equation numerical solution scheme is provided.

The application discloses a method for solving a second-order elliptic partial differential equation by combining a neural network and a finite element method. The method comprises the following steps: analyzing input parameter information of a second-order elliptic partial differential equation to be solved by using a target neural operator, and obtaining a corresponding solution network; feeding forward and calculating interpolation of discrete points of the solution network on each finite element unit of an object according to finite element unit information of a plurality of finite element units obtained by dividing the object, and obtaining a modified solution vector; modifying a solution vector of the second-order elliptic partial differential equation to be solved by using the modified solution vector, and iteratively processing the modified solution vector by using an iterative method; repeating the modification-iteration process until a preset convergence condition is met; and outputting the iterated solution vector. The application solves the technical problem that the related art needs to artificially construct a multi-grid to accelerate iteration when solving a second-order elliptic partial differential equation, resulting in high calculation cost and low solution accuracy.