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Frequency-resolved optical gating (FROG) is probably the most popular technique for complete characterization of ultrashort laser pulses. In FROG, a reconstruction algorithm retrieves the pulse from a measured spectrogram, yet current FROG…
We consider the problem of global optimization with noisy zeroth order oracles - a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
High-fidelity flow simulations are indispensable when analyzing systems exhibiting multiphase flow phenomena. The accuracy of multiphase flow simulations is strongly contingent upon the finest mesh resolution used to represent the…
We describe an optical simulation program that models a complete, coupled-cavity interferometer like those used by the Laser Interferometer Gravitational-Wave Observatory (LIGO) Project. A wide variety of interferometer deformations can be…
The paper presents an ab initio account of the paraxial complex geometrical optics (CGO) in application to a scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic…
Inverse rendering of glossy objects from RGB imagery remains fundamentally limited by inherent ambiguity. Although NeRF-based methods achieve high-fidelity reconstruction via dense-ray sampling, their computational cost is prohibitive.…
We consider a smoothed online convex optimization (SOCO) problem with predictions, where the learner has access to a finite lookahead window of time-varying stage costs, but suffers a switching cost for changing its actions at each stage.…
Bayesian optimization (BO) has been widely used in machine learning and simulation optimization. With the increase in computational resources and storage capacities in these fields, high-dimensional and large-scale problems are becoming…
Traditional approaches to portfolio optimization, often rooted in Modern Portfolio Theory and solved via quadratic programming or evolutionary algorithms, struggle with scalability or flexibility, especially in scenarios involving complex…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
Diffusion models have shown remarkable flexibility for solving inverse problems without task-specific retraining. However, existing approaches such as Manifold Preserving Guided Diffusion (MPGD) apply only a single gradient update per…
In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we relax both the Fourier magnitudes and object constraints.…
Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and…
A hybrid physical and geometrical optics method is proposed to model the subsurface imaging using mmWave FMCW radar. Modeling of the wave propagation for subsurface imaging can improve the interpretation of acquired data and imaging…
Optical molecular tomographic imaging is to reconstruct the concentration distribution of photon-molecular probes in a small animal from measured photon fluence rates. The localization and quantification of molecular probes is related to…
"Classical" First Order (FO) algorithms of convex optimization, such as Mirror Descent algorithm or Nesterov's optimal algorithm of smooth convex optimization, are well known to have optimal (theoretical) complexity estimates which do not…
Molecular property optimization (MPO) problems are inherently challenging since they are formulated over discrete, unstructured spaces and the labeling process involves expensive simulations or experiments, which fundamentally limits the…
Global MCAO aims to exploit a very wide technical field of view to find AO-suitable NGSs, with the goal to increase the overall sky coverage. The concept foresees the use of numerical entities, called Virtual Deformable Mirrors, to deal…
Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a…