Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.
Approximation capabilities of multilayer feedforward networks.Neural Networks, 4(2):251–257, 1991
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Neural network emulators of Grad-Shafranov equilibria enable real-time derivation of virtual circuits that disentangle plasma shape control parameters in tokamaks.
Real-world signals occupy compact low-variability regions in functional space, supplying a topological basis for perception, identifiability, and generalization from few examples.
citing papers explorer
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Learning on the Temporal Tangent Bundle for Physics-Informed Neural Networks
Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.
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Real-time virtual circuits for plasma shape control via neural network emulators
Neural network emulators of Grad-Shafranov equilibria enable real-time derivation of virtual circuits that disentangle plasma shape control parameters in tokamaks.
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The Blueprints of Intelligence: A Functional-Topological Foundation for Perception and Representation
Real-world signals occupy compact low-variability regions in functional space, supplying a topological basis for perception, identifiability, and generalization from few examples.