466,986 research outputs found
The identification of a distributed parameter model for a flexible structure
A computational method is developed for the estimation of parameters in a distributed model for a flexible structure. The structure we consider (part of the RPL experiment) consists of a cantilevered beam with a thruster and linear accelerometer at the free end. The thruster is fed by a pressurized hose whose horizontal motion effects the transverse vibration of the beam. The Euler-Bernoulli theory is used to model the vibration of the beam and treat the hose-thruster assembly as a lumped or point mass-dashpot-spring system at the tip. Using measurements of linear acceleration at the tip, it is estimated that the parameters (mass, stiffness, damping) and a Voight-Kelvin viscoelastic structural damping parameter for the beam using a least squares fit to the data. Spline based approximations to the hybrid (coupled ordinary and partial differential equations) system are considered; theoretical convergence results and numerical studies with both simulation and actual experimental data obtained from the structure are presented and discussed
High-Dimensional Dependency Structure Learning for Physical Processes
In this paper, we consider the use of structure learning methods for
probabilistic graphical models to identify statistical dependencies in
high-dimensional physical processes. Such processes are often synthetically
characterized using PDEs (partial differential equations) and are observed in a
variety of natural phenomena, including geoscience data capturing atmospheric
and hydrological phenomena. Classical structure learning approaches such as the
PC algorithm and variants are challenging to apply due to their high
computational and sample requirements. Modern approaches, often based on sparse
regression and variants, do come with finite sample guarantees, but are usually
highly sensitive to the choice of hyper-parameters, e.g., parameter
for sparsity inducing constraint or regularization. In this paper, we present
ACLIME-ADMM, an efficient two-step algorithm for adaptive structure learning,
which estimates an edge specific parameter in the first step,
and uses these parameters to learn the structure in the second step. Both steps
of our algorithm use (inexact) ADMM to solve suitable linear programs, and all
iterations can be done in closed form in an efficient block parallel manner. We
compare ACLIME-ADMM with baselines on both synthetic data simulated by partial
differential equations (PDEs) that model advection-diffusion processes, and
real data (50 years) of daily global geopotential heights to study information
flow in the atmosphere. ACLIME-ADMM is shown to be efficient, stable, and
competitive, usually better than the baselines especially on difficult
problems. On real data, ACLIME-ADMM recovers the underlying structure of global
atmospheric circulation, including switches in wind directions at the equator
and tropics entirely from the data.Comment: 21 pages, 8 figures, International Conference on Data Mining 201
Hierarchical adaptive low-rank format with applications to discretized partial differential equations
A novel framework for hierarchical low-rank matrices is proposed that combines an adaptive hierarchical partitioning of the matrix with low-rank approximation. One typical application is the approximation of discretized functions on rectangular domains; the flexibility of the format makes it possible to deal with functions that feature singularities in small, localized regions. To deal with time evolution and relocation of singularities, the partitioning can be dynamically adjusted based on features of the underlying data. Our format can be leveraged to efficiently solve linear systems with Kronecker product structure, as they arise from discretized partial differential equations (PDEs). For this purpose, these linear systems are rephrased as linear matrix equations and a recursive solver is derived from low-rank updates of such equations. We demonstrate the effectiveness of our framework for stationary and time-dependent, linear and nonlinear PDEs, including the Burgers' and Allen-Cahn equations
Neural ODEs as a discovery tool to characterize the structure of the hot galactic wind of M82
Dynamic astrophysical phenomena are predominantly described by differential
equations, yet our understanding of these systems is constrained by our
incomplete grasp of non-linear physics and scarcity of comprehensive datasets.
As such, advancing techniques in solving non-linear inverse problems becomes
pivotal to addressing numerous outstanding questions in the field. In
particular, modeling hot galactic winds is difficult because of unknown
structure for various physical terms, and the lack of \textit{any} kinematic
observational data. Additionally, the flow equations contain singularities that
lead to numerical instability, making parameter sweeps non-trivial. We leverage
differentiable programming, which enables neural networks to be embedded as
individual terms within the governing coupled ordinary differential equations
(ODEs), and show that this method can adeptly learn hidden physics. We robustly
discern the structure of a mass-loading function which captures the physical
effects of cloud destruction and entrainment into the hot superwind. Within a
supervised learning framework, we formulate our loss function anchored on the
astrophysical entropy (). Our results demonstrate the
efficacy of this approach, even in the absence of kinematic data . We then
apply these models to real Chandra X-Ray observations of starburst galaxy M82,
providing the first systematic description of mass-loading within the
superwind. This work further highlights neural ODEs as a useful discovery tool
with mechanistic interpretability in non-linear inverse problems. We make our
code public at this GitHub repository
(https://github.com/dustindnguyen/2023_NeurIPS_NeuralODEs_M82).Comment: 9 Pages, 2 Figures, Accepted at the NeurIPS 2023 workshop on Machine
Learning and the Physical Science
A Reduced-Order Model Bi-Modal Excitation of a Supersonic Planar Jet
This work analytically and numerically examines the effects of bi-modal excitation on a Mach 1.5 heated planar jet. Starting with the Navier-Stokes equations, triple decomposition is applied to the flow components. A reduced order model is derived, turning the Navier-Stokes partial differential equations into a set of coupled ordinary differential equations, relating the momentum thickness and amplitudes of a fundamental and subharmonic mode to the streamwise location along the jet. Computational fluid dynamics data from the minor plane of a Mach 1.5 heated rectangular jet is used to verify a hyperbolic tangent profile for the mean flow at various streamwise locations. Locallyparallel linear stability theory is used to compute the shape assumptions for the coherent structure components involved in the set of ordinary differential equations. The set of ordinary differential equations is first solved for a single mode. The trends for the single mode excitation qualitatively compared well with previous work. In the initial region, the nonlinear amplitude generally agreed well with the linear solution. Bi-modal excitation is then examined for the fundamental Strouhal number 0.10, which has been identified as a dominant noise source. Cases were considered separately with adding the subharmonic and the harmonic as a means of reducing the amplitude of the fundamental. Adding the subharmonic had minimal effects on reducing the fundamental unless both initial amplitudes are large. However, adding the harmonic could be very effective at reducing the fundamental even at low initial amplitudes. It is ultimately determined that adding the subharmonic may or may not be effective as a noise-reducing mechanism but adding the harmonic can be effective depending on the initial phase difference between the two excitations
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