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1. Embedding properties of network realizations of dissipative reduced order models

   Druskin, Guddati ( July 2022 , HOUSEHOLDER SYMPOSIUM XXI)

   Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and block-tridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistor-capacitor-inductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to so-called nite-dierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM state-space representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from the transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a non-symmetric Lanczos algorithm written in J-symmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nite-dierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich data-manifolds), a nite-dierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in port-Hamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible non-positivity of conductors for the non-Stieltjes case, we introduce an additional complex s-dependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on Krein-Nudelman theory [5], that results in special data-driven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the three-point second dierences: I. A two-point positive denite problem in a semi-innite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graph-Laplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go back 

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2. An Interpretable Machine-learning Framework for Modeling High-resolution Spectroscopic Data*

   https://doi.org/10.3847/1538-4357/aca0a2  

   Gully-Santiago, Michael ; Morley, Caroline V. ( December 2022 , The Astrophysical Journal)

   Comparison of échelle spectra to synthetic models has become a computational statistics challenge, with over 10,000 individual spectral lines affecting a typical cool star échelle spectrum. Telluric artifacts, imperfect line lists, inexact continuum placement, and inflexible models frustrate the scientific promise of these information-rich data sets. Here we debut an interpretable machine-learning frameworkblaséthat addresses these and other challenges. The semiempirical approach can be viewed as “transfer learning”—first pretraining models on noise-free precomputed synthetic spectral models, then learning the corrections to line depths and widths from whole-spectrum fitting to an observed spectrum. The auto-differentiable model employs back-propagation, the fundamental algorithm empowering modern deep learning and neural networks. Here, however, the 40,000+ parameters symbolize physically interpretable line profile properties such as amplitude, width, location, and shape, plus radial velocity and rotational broadening. This hybrid data-/model-driven framework allows joint modeling of stellar and telluric lines simultaneously, a potentially transformative step forward for mitigating the deleterious telluric contamination in the near-infrared. Theblaséapproach acts as both a deconvolution tool and semiempirical model. The general-purpose scaffolding may be extensible to many scientific applications, including precision radial velocities, Doppler imaging, chemical abundances for Galactic archeology, line veiling, magnetic fields, and remote sensing. Its sparse-matrix architecture and GPU acceleration makeblaséfast. The open-source PyTorch-based codeblaseincludes tutorials, Application Programming Interface documentation, and more. We show how the tool fits into the existing Python spectroscopy ecosystem, demonstrate a range of astrophysical applications, and discuss limitations and future extensions.

    

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3. Rep-Net: Efficient On-Device Learning via Feature Reprogramming

   Yang, Li ; Rakin, Adnan Siraj ; Fan, Deliang ( June 2022 , IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR))

   Transfer learning, where the goal is to transfer the well-trained deep learning models from a primary source task to a new task, is a crucial learning scheme for on-device machine learning, due to the fact that IoT/edge devices collect and then process massive data in our daily life. However, due to the tiny memory constraint in IoT/edge devices, such on-device learning requires ultra-small training memory footprint, bringing new challenges for memory-efficient learning. Many existing works solve this problem by reducing the number of trainable parameters. However, this doesn't directly translate to memory-saving since the major bottleneck is the activations, not parameters. To develop memory-efficient on-device transfer learning, in this work, we are the first to approach the concept of transfer learning from a new perspective of intermediate feature reprogramming of a pre-trained model (i.e., backbone). To perform this lightweight and memory-efficient reprogramming, we propose to train a tiny Reprogramming Network (Rep-Net) directly from the new task input data, while freezing the backbone model. The proposed Rep-Net model interchanges the features with the backbone model using an activation connector at regular intervals to mutually benefit both the backbone model and Rep-Net model features. Through extensive experiments, we validate each design specs of the proposed Rep-Net model in achieving highly memory-efficient on-device reprogramming. Our experiments establish the superior performance (i.e., low training memory and high accuracy) of Rep-Net compared to SOTA on-device transfer learning schemes across multiple benchmarks. 

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4. Sim2Sim Evaluation of a Novel Data-Efficient Differentiable Physics Engine for Tensegrity Robots

   Wang, Kun ; Aanjaneya, Mridul ; Bekris, Kostas E ( September 2021 , IEEE/RSJ International Conference on Intelligent Robots and Systems)

   null (Ed.)

   Learning policies in simulation is promising for reducing human effort when training robot controllers. This is especially true for soft robots that are more adaptive and safe but also more difficult to accurately model and control. The sim2real gap is the main barrier to successfully transfer policies from simulation to a real robot. System identification can be applied to reduce this gap but traditional identification methods require a lot of manual tuning. Data-driven alternatives can tune dynamical models directly from data but are often data hungry, which also incorporates human effort in collecting data. This work proposes a data-driven, end-to-end differentiable simulator focused on the exciting but challenging domain of tensegrity robots. To the best of the authors’ knowledge, this is the first differentiable physics engine for tensegrity robots that supports cable, contact, and actuation modeling. The aim is to develop a reasonably simplified, data-driven simulation, which can learn approximate dynamics with limited ground truth data. The dynamics must be accurate enough to generate policies that can be transferred back to the ground-truth system. As a first step in this direction, the current work demonstrates sim2sim transfer, where the unknown physical model of MuJoCo acts as a ground truth system. Two different tensegrity robots are used for evaluation and learning of locomotion policies, a 6-bar and a 3-bar tensegrity. The results indicate that only 0.25% of ground truth data are needed to train a policy that works on the ground truth system when the differentiable engine is used for training against training the policy directly on the ground truth system. 

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5. Estimating Full Longwave and Shortwave Radiative Transfer with Neural Networks of Varying Complexity

   https://doi.org/10.1175/JTECH-D-23-0012.1  

   Lagerquist, Ryan ; Turner, David D. ; Ebert-Uphoff, Imme ; Stewart, Jebb Q. ( November 2023 , Journal of Atmospheric and Oceanic Technology)

   Radiative transfer (RT) is a crucial but computationally expensive process in numerical weather/climate prediction. We develop neural networks (NN) to emulate a common RT parameterization called the Rapid Radiative Transfer Model (RRTM), with the goal of creating a faster parameterization for the Global Forecast System (GFS) v16. In previous work we emulated a highly simplified version of the shortwave RRTM only—excluding many predictor variables, driven by Rapid Refresh forecasts interpolated to a consistent height grid, using only 30 sites in the Northern Hemisphere. In this work we emulate the full shortwave and longwave RRTM—with all predictor variables, driven by GFSv16 forecasts on the native pressure–sigma grid, using data from around the globe. We experiment with NNs of widely varying complexity, including the U-net++ and U-net3+ architectures and deeply supervised training, designed to ensure realistic and accurate structure in gridded predictions. We evaluate the optimal shortwave NN and optimal longwave NN in great detail—as a function of geographic location, cloud regime, and other weather types. Both NNs produce extremely reliable heating rates and fluxes. The shortwave NN has an overall RMSE/MAE/bias of 0.14/0.08/−0.002 K day⁻¹for heating rate and 6.3/4.3/−0.1 W m⁻²for net flux. Analogous numbers for the longwave NN are 0.22/0.12/−0.0006 K day⁻¹and 1.07/0.76/+0.01 W m⁻². Both NNs perform well in nearly all situations, and the shortwave (longwave) NN is 7510 (90) times faster than the RRTM. Both will soon be tested online in the GFSv16.

   Radiative transfer is an important process for weather and climate. Accurate radiative transfer models exist, such as the RRTM, but these models are computationally slow. We develop neural networks (NNs), a type of machine learning model that is often computationally fast after training, to mimic the RRTM. We wish to accelerate the RRTM by orders of magnitude without sacrificing much accuracy. We drive both the NNs and RRTM with data from the GFSv16, an operational weather model, using locations around the globe during all seasons. We show that the NNs are highly accurate and much faster than the RRTM, which suggests that the NNs could be used to solve radiative transfer inside the GFSv16.

    

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