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Data mining for faster, interpretable solutions to inverse problems: A case study using additive manufacturing
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Extraction of interaction parameters from specular neutron reflectivity in thin films of diblock copolymers: an “inverse problem”
Artificial neural networks are used to extract three Flory-Huggins chi parameters from neutron scattering length density profiles, which paves a way towards automated analysis of neutron reflectivity data.
TTVFast: An efficient and accurate code for transit timing inversion problems
Transit timing variations (TTVs) have proven to be a powerful technique for confirming Kepler planet candidates, for detecting non-transiting planets, and for constraining the masses and orbital elements of multi-planet systems. These TTV applications often require the numerical integration of orbits for computation of transit times (as well as impact parameters and durations); frequently tens of millions to billions of simulations are required when running statistical analyses of the planetary system properties. We have created a fast code for transit timing computation, TTVFast, which uses a symplectic integrator with a Keplerian interpolator for the calculation of transit times. The speed comes at the expense of accuracy in the calculated times, but the accuracy lost is largely unnecessary, as transit times do not need to be calculated to accuracies significantly smaller than the measurement uncertainties on the times. The time step can be tuned to give sufficient precision for any particular system. We find a speed-up of at least an order of magnitude relative to dynamical integrations with high precision using a Bulirsch-Stoer integrator.
An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems
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Uniform-density Bose-Einstein condensates of the Gross-Pitaevskii equation found by solving the inverse problem for the confining potential
Here, in this work, we consider a “reverse-engineering” approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevskii equation (GPE) also known as the nonlinear Schr¨odinger equation (NLSE). In the one-dimensional case, the exact solution is the sum of stationary kink and anti-kink solutions, i.e. a kovaton, and in the overlapping region, the density is constant. In higher dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed out finite square well with minima also at the edges. When self-interactions are added, a term proportional to ±gψ*ψ gets added to the confining potential and ±gM, where M is the norm, gets added to the total energy. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M (related to the number of particles in the BEC). Comparing the stability criteria from Derrick’s theorem and Bogoliubov-de Gennes analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. The numerical analysis shows further that the initial instabilities violate the symmetry x → -x assumed by Derrick’s theorem.
Using Deep Neural Networks for Inverse Problems in Imaging: Beyond Analytical Methods
Not provided.
CoIL: Coordinate-based Internal Learning for Imaging Inverse Problems
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Massively Parallel Structural Acoustics for Forward and Inverse Problems.
Abstract not provided.
A Data Scalable Augmented Lagrangian KKT Preconditioner for Large-Scale Inverse Problems
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Preconditioned Pseudo-time Continuation for Parameterized Inverse Problems
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Inverse problem: What can we tell about the matter and energy in our Universe from its dimensionality and evolution
The most well-known theories of everything are assorted versions of the superstring theory. The theories require existence of additional space dimensions, vibrations of which create the material particles in 3D space. The additional space dimensions are understood as being currently smaller than the Planck Length and due to this not directly observable. We search for multidimensional models of the Universe (one time dimension; three isotropic, flat external dimensions, and n-internal dimensions), which satisfy the multidimensional Einstein equations and which started from the same radius of all of the internal and external dimensions, with an anisotropic energy–momentum tensor. Analytical solution of (N+1)-dimensional Einstein equation in a reparameterized time is reminded and discussed. The energy–momentum tensor is solely responsible for expansion of the external dimensions and shrinking of the internal ones; and to obtain this behavior of the space the tensor needs to fulfill some conditions i.e. the energy–momentum tensor cannot include only radiation, vacuum and baryonic matter. For the behavior of the physical space consistent with the one observed in our Universe, the dark energy and/or dark matter have to exist.
Active Subspace Methods for Data-Intensive Inverse Problems
The project has developed theory and computational tools to exploit active subspaces to reduce the dimension in statistical calibration problems. This dimension reduction enables MCMC methods to calibrate otherwise intractable models. The same theoretical and computational tools can also reduce the measurement dimension for calibration problems that use large stores of data.
Predictive Modeling, Inverse Problems, and Uncertainty Quantification with Application to Emergency Response
No abstract provided.
Variational Methods for Posterior Estimation of Non-linear Inverse Problems
No abstract provided.