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Physics-informed neural networks for solving Navier–Stokes equations. Physics-informed neural networks (PINNs), [1] also referred to as Theory-Trained Neural Networks (TTNs), [2] are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs).
Physics informed neural networks have been used to solve partial differential equations in both forward and inverse problems in a data driven manner. [36] One example is the reconstructing fluid flow governed by the Navier-Stokes equations .
A physical neural network is a type of artificial neural network in which an electrically adjustable material is used to emulate the function of a neural synapse or a higher-order (dendritic) neuron model. [1] "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate neurons as opposed to software-based ...
Deep learning is a subset of machine learning that focuses on utilizing neural networks to perform tasks such as classification, regression, and representation learning.The field takes inspiration from biological neuroscience and is centered around stacking artificial neurons into layers and "training" them to process data.
A key difference lies in communication between the layers of a neural networks. For classical neural networks, at the end of a given operation, the current perceptron copies its output to the next layer of perceptron(s) in the network. However, in a quantum neural network, where each perceptron is a qubit, this would violate the no-cloning theorem.
Networks such as the previous one are commonly called feedforward, because their graph is a directed acyclic graph. Networks with cycles are commonly called recurrent. Such networks are commonly depicted in the manner shown at the top of the figure, where is shown as dependent upon itself. However, an implied temporal dependence is not shown.
Some artificial neural networks are adaptive systems and are used for example to model populations and environments, which constantly change. Neural networks can be hardware- (neurons are represented by physical components) or software-based (computer models), and can use a variety of topologies and learning algorithms.
Neural network pushdown automata (NNPDA) are similar to NTMs, but tapes are replaced by analog stacks that are differentiable and trained. In this way, they are similar in complexity to recognizers of context free grammars (CFGs). [76] Recurrent neural networks are Turing complete and can run arbitrary programs to process arbitrary sequences of ...