Extreme Learning Machines as Encoders for Sparse Reconstruction
AbstractReconstruction of fine-scale information from sparse data is often needed in practical fluid dynamics where the sensors are typically sparse and yet, one may need to learn the underlying flow structures or inform predictions through assimilation into data-driven models. Given that sparse reconstruction is inherently an ill-posed problem, the most successful approaches encode the physics into an underlying sparse basis space that spans the manifold to generate well-posedness. To achieve this, one commonly uses a generic orthogonal Fourier basis or a data specific proper orthogonal decomposition (POD) basis to reconstruct from sparse sensor information at chosen locations. Such a reconstruction problem is well-posed as long as the sensor locations are incoherent and can sample the key physical mechanisms. The resulting inverse problem is easily solved using
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Al Mamun, S.M.A.; Lu, C.; Jayaraman, B. Extreme Learning Machines as Encoders for Sparse Reconstruction. Fluids 2018, 3, 88.
Al Mamun SMA, Lu C, Jayaraman B. Extreme Learning Machines as Encoders for Sparse Reconstruction. Fluids. 2018; 3(4):88.Chicago/Turabian Style
Al Mamun, S M.A.; Lu, Chen; Jayaraman, Balaji. 2018. "Extreme Learning Machines as Encoders for Sparse Reconstruction." Fluids 3, no. 4: 88.