Abstract: Methods and apparatuses that generate a simulation object for a physical system are described. The simulation object includes a trained computing structure to determine future output data of the physical system in real time. The computing structure is trained with a plurality of input units and one or more output units. The plurality of input units include regular input units to receive input data and output data of the physical system. The output units include one or more regular output units to predict a dynamic rate of change of the input data over a period of time. The input data and output data of the physical system are obtained for training the computing structure. The input data represent a dynamic input excitation to the physical system over the period of time. And the output data represents a dynamic output response of the physical system to the dynamic input excitation over the period of time.

Abstract: A method for building a neural network configured to be run on a destination computing unit is implemented by a system including a computer and a memory storing a learning dataset. The method includes providing a neural network having an initial topology, and training the initial topology over the learning dataset. The topology of the neural network is optimized, which includes at least one iteration of the following steps: for each of a plurality of candidate topological changes, estimating the variation induced by the candidate topological change on: the neural network's error, and a value of at least one physical quantity needed for executing the neural network on the destination processing unit, selecting at least one of the candidate topological changes based on said estimation and updating the topology of the neural network according to said selected topological change, and training the updated neural network over the learning dataset.

Abstract: A method of construction of a feedforward neural network includes a step of initialization of a neural network according to an initial topology, and at least one topological optimization phase, of which each phase includes: an additive phase including a modification of the network topology by adding at least one node and/or a connection link between the input of a node of a layer and the output of a node of any one of the preceding layers, and/or a subtractive phase including a modification of the network topology by removing at least one node and/or a connection link between two layers. Each topology modification includes the selection of a topology modification among several candidate modifications, based on an estimation of the variation in the network error between the previous topology and each topology modified according to a candidate modification.

Abstract: A method modeling a physical process in a material environment. A system of modeling equations at the level of each of the grid cells of a grid pattern involves a number n of cells subdividing the environment. The model is achieved at a relatively low cost and within a reasonable calculating time in relation to the quality and the accuracy of the simulations obtained, mainly by reducing the size of the solution problem. To that effect, a Krylov space of dimension d, much smaller than the number n of grid cells, is used. This has the effect of reducing the volume of the solution operations. The method can be used for modeling of fluid flow in an underground reservoir of, for example, hydrocarbons.

Abstract: A power distributor for microwave signals has n inputs and n outputs, n/2 coupler elements, four power distributor elements each having n/2 inputs and n/2 outputs. The inputs of the first and third distributor elements correspond to respective inputs of the distributor and the outputs of the second and fourth distributor elements correspond to respective outputs of the distributor. The outputs of the first distributor element are connected to respective first inputs of the couplers and the outputs of the third distributor element are connected to respective second inputs of the couplers. The inputs of the second distributor element are connected to respective first outputs of the couplers and the inputs of the fourth distributor element are connected to respective second outputs of the couplers.