MathDB3 problems
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The IBDL conjecture on differential operators and numerical Green's functions
The immersed boundary double layer method uses spread and interpolation operators together with discrete differential operators for solving Brinkman and Stokes equations. In partic…
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Existence of a condensed subspace with similar approximation performance for nonlinear PDEs
Condensed-subspace conjecture. A solution exists on a “condensed” subspace that can achieve similar approximation performance, and the optimization problem can therefore be reformu…
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Existence of a deep learning method overcoming the curse of dimensionality for PDEs
Let PDEs be numerical approximation problems, and let the curse of dimensionality refer to the unfavorable growth of computational complexity with the dimension of the underlying p…