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Similarity Metrics for Closed Loop Dynamic Systems

To what extent and in what ways can two closed-loop dynamic systems be said to be "similar?" This question arises in a wide range of dynamic systems modeling and control system design applications. For example, bounds on error models are fundamental to the controller optimization with modern control design methods. Metrics such as the structured singular value are direct measures of the degree to which properties such as stability or performance are maintained in the presence of specified uncertainties or variations in the plant model. Similarly, controls-related areas such as system identification, model reduction, and experimental model validation employ measures of similarity between multiple realizations of a dynamic system. Each area has its tools and approaches, with each tool more or less suited for one application or the other. Similarity in the context of closed-loop model validation via flight test is subtly different from error measures in the typical controls oriented application. Whereas similarity in a robust control context relates to plant variation and the attendant affect on stability and performance, in this context similarity metrics are sought that assess the relevance of a dynamic system test for the purpose of validating the stability and performance of a "similar" dynamic system. Similarity in the context of system identification is much more relevant than are robust control analogies in that errors between one dynamic system (the test article) and another (the nominal "design" model) are sought for the purpose of bounding the validity of a model for control design and analysis. Yet system identification typically involves open-loop plant models which are independent of the control system (with the exception of limited developments in closed-loop system identification which is nonetheless focused on obtaining open-loop plant models from closed-loop data). Moreover the objectives of system identification are not the same as a flight test and hence system identification error metrics are not directly relevant. In applications such as launch vehicles where the open loop plant is unstable it is similarity of the closed-loop system dynamics of a flight test that are relevant.

Whorton, Mark S.↗

The Power of Many: An Ensemble Approach to Spectral Similarity

Quantifying the similarity between two mass spectra─a known reference mass spectrum and an unidentified sample mass spectrum─is at the heart of compound identification workflows in gas chromatography–mass spectrometry (GC-MS). The reference spectrum most like the sample is assigned as its identification (provided some quantitative similarity threshold is met, e.g., 80%) and thus accurately measuring similarity is essential. Significant research has gone toward developing metrics for this purpose, each of which has attempted to improve upon existing methods by incorporating GC-MS-specific information (e.g., peak ratios or retention times) or adopting various statistical and algorithmic frameworks. While this active development has led to a plethora of similarity metrics with demonstrated value across different contexts, the unfortunate consequence has been confusion surrounding which metric should be used as a global standard. No such metric is currently accepted as the standard method because different metrics have demonstrated optimal performance in different contexts. In this work, we propose an ensemble approach to spectral similarity scoring that combines the collective information from across existing similarity metrics to form an improved, globally representative similarity metric as a step toward establishing a global standard method. In conclusion, the resulting ensemble metrics are evaluated on over 88,000 spectra of varying complexity and demonstrate improved abilities to accurately rank the correct reference spectrum as the top-matching candidate for a sample relative to the rankings generated by individual similarity scores.

Carbohydrates↗

A similarity hypothesis for the two-point correlation tensor in a temporally evolving plane wake

The analysis demonstrated that the governing equations for the two-point velocity correlation tensor in the temporally evolving wake admit similarity solutions, which include the similarity solutions for the single-point moment as a special case. The resulting equations for the similarity solutions include two constants, beta and Re(sub sigma), that are ratios of three characteristic time scales of processes in the flow: a viscous time scale, a time scale characteristic of the spread rate of the flow, and a characteristic time scale of the mean strain rate. The values of these ratios depend on the initial conditions of the flow and are most likely measures of the coherent structures in the initial conditions. The occurrences of these constants in the governing equations for the similarity solutions indicates that these solutions, in general, will only be the same for two flows if these two constants are equal (and hence the coherent structures in the flows are related). The comparisons between the predictions of the similarity hypothesis and the data presented here and elsewhere indicate that the similarity solutions for the two-point correlation tensors provide a good approximation of the measures of those motions that are not significantly affected by the boundary conditions caused by the finite extent of real flows. Thus, the two-point similarity hypothesis provides a useful tool for both numerical and physical experimentalist that can be used to examine how the finite extent of real flows affect the evolution of the different scales of motion in the flow.

Ewing, D. W.↗

Similarity Assessment of Land Surface Model Outputs in the North American Land Data Assimilation System

Multimodel ensembles are often used to produce ensemble mean estimates that tend to have increased simulation skill over any individual model output. If multimodel outputs are too similar, an individual LSM would add little additional information to the multimodel ensemble, whereas if the models are too dissimilar, it may be indicative of systematic errors in their formulations or configurations. The article presents a formal similarity assessment of the North American Land Data Assimilation System (NLDAS) multimodel ensemble outputs to assess their utility to the ensemble, using a confirmatory factor analysis. Outputs from four NLDAS Phase 2 models currently running in operations at NOAA/NCEP and four new/ upgraded models that are under consideration for the next phase of NLDAS are employed in this study. The results show that the runoff estimates from the LSMs were most dissimilar whereas the models showed greater similarity for root zone soil moisture, snow water equivalent, and terrestrial water storage. Generally, the NLDAS operational models showed weaker association with the common factor of the ensemble and the newer versions of the LSMs showed stronger association with the common factor, with the model similarity increasing at longer time scales. Trade-offs between the similarity metrics and accuracy measures indicated that the NLDAS operational models demonstrate a larger span in the similarity-accuracy space compared to the new LSMs. The results of the article indicate that simultaneous consideration of model similarity and accuracy at the relevant time scales is necessary in the development of multimodel ensemble.

land surface models↗

NMR Spectroscopy for Protein Higher Order Structure Similarity Assessment in Formulated Drug Products

Peptide and protein drug molecules fold into higher order structures (HOS) in formulation and these folded structures are often critical for drug efficacy and safety. Generic or biosimilar drug products (DPs) need to show similar HOS to the reference product. The solution NMR spectroscopy is a non-invasive, chemically and structurally specific analytical method that is ideal for characterizing protein therapeutics in formulation. However, only limited NMR studies have been performed directly on marketed DPs and questions remain on how to quantitively define similarity. Here, NMR spectra were collected on marketed peptide and protein DPs, including calcitonin-salmon, liraglutide, teriparatide, exenatide, insulin glargine and rituximab. The 1D 1 H spectral pattern readily revealed protein HOS heterogeneity, exchange and oligomerization in the different formulations. Principal component analysis (PCA) applied to two rituximab DPs showed consistent results with the previously demonstrated similarity metrics of Mahalanobis distance (D M ) of 3.3. The 2D 1 H- 13 C HSQC spectral comparison of insulin glargine DPs provided similarity metrics for chemical shift difference (Δδ) and methyl peak profile, i.e., 4 ppb for 1 H, 15 ppb for 13 C and 98% peaks with equivalent peak height. Finally, 2D 1 H- 15 N sofast HMQC was demonstrated as a sensitive method for comparison of small protein HOS. The application of NMR procedures and chemometric analysis on therapeutic proteins offer quantitative similarity assessments of DPs with practically achievable similarity metrics.

59 BASIC BIOLOGICAL SCIENCES↗

Neural architecture search via similarity adaptive guidance

Evolutionary neural network architecture search (ENAS) has attracted the attention of many experts due to its global optimization capabilities to automatically search for convolutional neural network architectures based on the target task. The current search space for ENAS is not to design a fully structured network, but to search for smaller cell architectures to reduce search costs. However, blind search strategies do not effectively utilize the potential experience of the population. In order to utilize the potential experience learned by the current population to guide the evolutionary search of the population, we propose a similarity guided neural network architecture search algorithm based on cell architecture, which utilizes the similarity between pairwise architectures in the population as empirical knowledge learned by the population. Our proposed algorithm provides a novel method for calculating architecture similarity, which calculates architecture similarity separately from the cell and macro-structure. Then we decouple the connections and operations in the cell and calculate connection and operation similarity separately. In addition, we propose adaptive similarity selection and binary tournament selection strategies to enhance the algorithm’s global and local search capabilities and effectively explore the search space. Finally, we design an improved single-point crossover operator to enhance the local search ability of the evolutionary operator. The experimental results show that SAGNAS is a competitive algorithm that achieves 97.44% and 81.60% in CIFAR10 and CIFAR100 with only 1.9 GPU-days spent.

97 MATHEMATICS AND COMPUTING↗

Generalizing Similarity Laws for Radio-Frequency Discharge Plasmas across Nonlinear Transition Regimes

We generalize similarity theory based on the scaling and solution invariance of the Boltzmann equation, coupled with the Poisson equation, and demonstrate similarity laws for radio-frequency (rf) discharge plasmas across three nonlinear transitional regimes, namely, the alpha-gamma mode transition, the stochastic-Ohmic-heating mode transition, and the bounce-resonance-heating mode transition. Fundamental plasma parameters, e.g., the electron power absorption, under similar discharge conditions are examined via fully kinetic particle-in-cell simulations, and electron-kinetic invariance is exemplified in similar rf discharge plasmas. The results unambiguously confirm the applicability of similarity laws for rf plasmas in extended operating regimes, and strengthen the foundations and framework of similarity physics with universality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimizing FPGA-based Accelerator Design for Large-Scale Molecular Similarity Search (Special Session Paper)

Molecular similarity search has been widely used in drug discovery to rapidly identify structurally similar compounds from large molecular databases. With the increasing size of chemical libraries, there is growing interest in the efficient ac- celeration of large-scale similarity search. Existing works mainly focus on CPU and GPU to accelerate the computation of Tatimoto coefficient in measuring the pairwise similarity between different molecular fingerprints. In this paper, we propose and optimize an FPGA-based accelerator design on exhaustive and approximate search algorithms. On exhaustive search using BitBound & fold- ing, we analyze the similarity cutoff and folding level relationship with search speedup and accuracy, and propose a scalable on- the-fly query engine on FPGAs to reduce the resource utilization and pipeline interval. We achieve a 450 million compounds-per- second processing throughput for a single query engine. On approximate search using hierarchical navigable small world (HNSW), a popular algorithm with high recall and query speed, we propose an FPGA-based graph traversal engine to utilize high throughput register array based priority queue and fine- grained distance calculation engine to increase the processing capability. Experimental results show that the proposed FPGA- based HNSW implementation achieves a 35× speedup than existing works on CPU. To the best of our knowledge, our FPGA- based implementation is the first attempt to accelerate molecular similarity search on FPGA and has the highest performance among existing approaches.

Peng, Hongwu↗

Evidence of Mixed Scaling for Mean Profile Similarity in the Stable Atmospheric Surface Layer

A new mixed scaling parameter Z = z/(Lh)1/2 is proposed for similarity in the stable atmospheric surface layer, where z is the height, L is the Obukhov length, and h is the boundary layer depth. In comparison with the parameter ζ = z/L from Monin–Obukhov similarity theory (MOST), the new parameter Z leads to improved mean profile similarity for wind speed and air temperature in large-eddy simulations. It also yields the same linear similarity relation for CASES-99 field measurements, including in the strongly stable (but still turbulent) regime where large deviations from MOST are observed. Results further suggest that similarity for turbulent energy dissipation rate depends on both Z and ζ. The proposed mixed scaling of Z and relevance of h can be explained by physical arguments related to the limit of z-less stratification that is reached asymptotically above the surface layer. The presented evidence and fitted similarity relations are promising, but the results and arguments are limited to a small sample of idealized stationary stable boundary layers. Here, corroboration is needed from independent datasets and analyses, including for complex and transient conditions not tested here.

54 ENVIRONMENTAL SCIENCES↗

On similarity solutions for turbulent and heated round jets

Commonly used empirical correlations for incompressible, heated round jets are shown to represent similarity solutions of the governing jet equations. These solutions give rise to self-similar eddy viscosities. Not all the similarity solutions are physically valid because some lead to zero eddy viscosities at the jet centerline. One physically valid solution is found to correlate best with round jet measurements and it gives a Gaussian error function description for the normalized mean velocity and temperature. Heat and momentum fluxes thus calculated are also in good agreement with measurements. Therefore, in addition to the classical similarity solution obtained by assuming constant eddy viscosity, another similarity solution to the jet equations is found where the eddy viscosity is self-similar.

So, R. M. C.↗

Use of an approximate similarity principle for the thermal scaling of a full-scale thrust augmenting ejector

Full temperature ejector model simulations are expensive, and difficult to implement experimentally. If an approximate similarity principle could be established, properly chosen performance parameters should be similar for both hot and cold flow tests if the initial Mach number and total pressures of the flow field are held constant. Existing ejector data is used to explore the utility of one particular similarity principle; the Munk and Prim similarity principle for isentropic flows. Static performance test data for a full-scale thrust augmenting ejector are analyzed for primary flow temperatures up to 1560 R. At different primary temperatures, exit pressure contours are compared for similarity. A nondimensional flow parameter is then used to eliminate primary nozzle temperature dependence and verify similarity between the hot and cold flow experiments.

Barankiewicz, Wendy S.↗

Use of an approximate similarity principle for the thermal scaling of a full-scale thrust augmenting ejector

Full temperature ejector model simulations are expensive, and difficult to implement experimentally. If an approximate similarity principle could be established, properly chosen performance parameters should be similar for both hot and cold flow tests if the initial Mach number and total pressures of the flow field are held constant. Existing ejector data is used to explore the utility of one particular similarity principle; the Munk and Prim similarity principle for isentropic flows. Static performance test data for a full-scale thrust augmenting ejector are analyzed for primary flow temperatures up to 1560 R. At different primary temperatures, exit pressure contours are compared for similarity. A nondimensional flow paramenter is then used to eliminate primary nozzle temperature dependence and verify similarity between the hot and cold flow experiments.

Barankiewicz, Wendy↗

A New Look at Self-Similarity in Strained Plane Wakes

In early experiments, A. J. Reynolds and J. F. Keffer sought to determine whether plane wakes of circular cylinders, when strained by a wind tunnel of varying cross-section, evolved in accordance with an analytically derived self-similar solution. As pointed out by Reynolds, for the strain geometry considered this self-similar solution indicated exponential growth of the viscous term in the mean momentum equation, a result which he interpreted as suggesting that such wakes would eventually relaminarize. The experimental results were found not to agree with the similarity theory and recent direct numerical simulations confirm this. However, a more general self-similar analysis of the kind suggested by W. K. George is found to lead to families of possible similarity solutions, some of which do indeed describe the observed flaw behavior. These equilibrium similarity solutions result from creating a balance in the governing equations by grouping certain terms. For these solutions the viscous terms can be retained in the analysis.

Rogers, Michael M.↗

AIMSim : An accessible cheminformatics platform for similarity operations on chemicals datasets

The recent advances in deep learning, generative modeling, and statistical learning have ushered in a renewed interest in traditional cheminformatics tools and methods. Quantifying molecular similarity is essential in molecular generative modeling, exploratory molecular synthesis campaigns, and drug-discovery applications to assess how new molecules differ from existing ones. Further, most tools target advanced users and lack general implementations accessible to the larger community. In this work, we introduce Artificial Intelligence Molecular Similarity (AIMSim), an accessible cheminformatics platform for performing similarity operations on collections of molecules called molecular datasets. AIMSim provides a unified platform to perform similarity-based tasks on molecular datasets, such as diversity quantification, outlier and novelty analysis, clustering, dimensionality reduction, and inter-molecular comparisons. AIMSim implements all major binary similarity metrics and molecular fingerprints and is provided as a Python package that includes support for command-line use as well as a Graphical User Interface for code-free utilization with fully interactive plots.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A biology-informed similarity metric for simulated patches of human cell membrane

Complex scientific inquiries rely increasingly upon large and autonomous multiscale simulation campaigns, which fundamentally require similarity metrics to quantify ‘sufficient’ changes among data and/or configurations. However, subject matter experts are often unable to articulate similarity precisely or in terms of well-formulated definitions, especially when new hypotheses are to be explored, making it challenging to design a meaningful metric. Furthermore, the key to practical usefulness of such metrics to enable autonomous simulations lies in in situ inference, which requires generalization to possibly substantial distributional shifts in unseen, future data. Here, we address these challenges in a cancer biology application and develop a meaningful similarity metric for ‘patches’—regions of simulated human cell membrane that express interactions between certain proteins of interest and relevant lipids. In the absence of well-defined conditions for similarity, we leverage several biology-informed notions about data and the underlying simulations to impose inductive biases on our metric learning framework, resulting in a suitable similarity metric that also generalizes well to significant distributional shifts encountered during the deployment. We combine these intuitions to organize the learned embedding space in a multiscale manner, which makes the metric robust to incomplete and even contradictory intuitions. Our approach delivers a metric that not only performs well on the conditions used for its development and other relevant criteria, but also learns key spatiotemporal relationships without ever being exposed to any such information during training.

97 MATHEMATICS AND COMPUTING↗

Impact of Thermal Scattering Law on Similarity Assessment in Light-Water or Polyethylene-Moderated Systems

A collaborative effort between Pacific Northwest National Laboratory (PNNL) and Oak Ridge National Laboratory (ORNL) is underway to provide a technical basis and methodology for the criticality safety community to use the sum of fractions (SoF) method for generating limits for mixtures of “selected actinide nuclides” included in the ANSI/ANS 8.15 standard. The PNNL scope in this project is to define a range of mixtures of 233 U, 235 U, and 239 Pu moderated with either light water or polyethylene and to examine the critical masses for these mixtures. The ORNL scope is primarily to provide validation support for these studies. More complete discussion of the project and its validation aspects will be presented at the upcoming International Conference on Nuclear Criticality Safety (ICNC) this Fall in Sendai, Japan. Clear differences in benchmark similarity to application systems as assessed by the integral parameter ck are noted in the validation studies performed as part of this project as a function of moderator. The c k value is a correlation coefficient that represents that amount of shared uncertainty in k eff due to cross sections between two systems. Individual nuclide-reaction contributions between the two systems can be simply summed to arrive at the total c k value. Specifically, the c k values for light-water–moderated solution experiments are higher for a water-moderated application than for a polyethylene-moderated application. This result is neither totally unexpected nor surprising, but the magnitude of the difference was difficult to anticipate. The TSUNAMI sequence, in the SCALE 6.2.4 code package developed by ORNL, was used to generate eigenvalues and reactivity effects with perturbation-theory based approach through sensitivity coefficients for all nuclides in the system with all reactions and energy groups. The TSUNAMI-Indices and Parameters (IP) sequence then uses the sensitivity data generated through TSUNAMI to generate relational parameters (i.e., c k ) to determine the degree of similarity between systems. One detail of the SCALE material and data implementation must be discussed at this point. Several thermal scattering laws (TSLs) are available for 1 H. SCALE uses a different nuclide ID number for each TSL; essentially, each version of 1 H is treated as a unique nuclide. For example, 1 H bound in water ( 1 H-H2O) is assigned the nuclide ID 1001, whereas 1 H bound in polyethylene (h-poly) is assigned the nuclide ID 9001001. The same cross section data are used for all reactions in 1 H, regardless of TSL, except for scattering below the TSL cutoff energy. TSUNAMI-IP treats different nuclide IDs as different nuclides; thus, no uncertainty is shared between 1 H-H2O and h-poly, despite much of the same data, including covariance data, being used for both nuclides. This presents a question: how much of the difference in assessed similarity between water- and polyethylene-moderated systems is due to the moderators, and how much is caused by the treatment of 1 H-H2O and h poly with cross section and covariance data. The extended edits generated by TSUANMI-IP allow for an investigation of this issue specifically, as well as a demonstration of the general techniques available within TSUNAMI to understand the results of the similarity assessment. This paper presents and analyzes the similarity assessment of both water- and polyethylene-moderated systems for a single benchmark: PST-002-001.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Combining pairwise structural similarity and deep learning interface contact prediction to estimate protein complex model accuracy in CASP15

Abstract Estimating the accuracy of quaternary structural models of protein complexes and assemblies (EMA) is important for predicting quaternary structures and applying them to studying protein function and interaction. The pairwise similarity between structural models is proven useful for estimating the quality of protein tertiary structural models, but it has been rarely applied to predicting the quality of quaternary structural models. Moreover, the pairwise similarity approach often fails when many structural models are of low quality and similar to each other. To address the gap, we developed a hybrid method (MULTICOM_qa) combining a pairwise similarity score (PSS) and an interface contact probability score (ICPS) based on the deep learning inter‐chain contact prediction for estimating protein complex model accuracy. It blindly participated in the 15th Critical Assessment of Techniques for Protein Structure Prediction (CASP15) in 2022 and performed very well in estimating the global structure accuracy of assembly models. The average per‐target correlation coefficient between the model quality scores predicted by MULTICOM_qa and the true quality scores of the models of CASP15 assembly targets is 0.66. The average per‐target ranking loss in using the predicted quality scores to rank the models is 0.14. It was able to select good models for most targets. Moreover, several key factors (i.e., target difficulty, model sampling difficulty, skewness of model quality, and similarity between good/bad models) for EMA are identified and analyzed. The results demonstrate that combining the multi‐model method (PSS) with the complementary single‐model method (ICPS) is a promising approach to EMA.

59 BASIC BIOLOGICAL SCIENCES↗

Establishing metrics to quantify spatial similarity in spherical and red blood cell distributions

As computational power increases and systems with millions of red blood cells can be simulated, it is important to note that varying spatial distributions of cells may affect simulation outcomes. Since a single simulation may not represent the ensemble behavior, many different configurations may need to be sampled to adequately assess the entire collection of potential cell arrangements. In order to determine both the number of distributions needed and which ones to run, we must first establish methods to identify well-generated, randomly placed cell distributions and to quantify distinct cell configurations. We utilize metrics to assess (1) the presence of any underlying structure to the initial cell distribution and (2) similarity between cell configurations. We propose the use of the radial distribution function to identify long-range structure in a cell configuration and apply it to a randomly distributed and structured set of red blood cells. To quantify spatial similarity between two configurations, we make use of the Jaccard index, and characterize sets of red blood cell and sphere initializations. As an extension to our work submitted to the International Conference on Computational Science, we significantly increase our data set size from 72 to 1048 cells, include a similar set of studies using spheres, compare the effects of varying sphere size, and utilize the Jaccard index distribution to probe sets of extremely similar configurations. Our results show that the radial distribution function can be used as a metric to determine long-range structure in both distributions of spheres and RBCs. We determine that the ideal case of spheres within a cube versus bi-concave shaped cells within a cylinder affects the shape of the Jaccard index distributions, as well as the range of Jaccard values, showing that both the shape of particle and the domain may play a role. Furthermore, we also find that the distribution is able to capture very similar configurations through Jaccard index values greater than 95% when appending several nearly identical configurations into the data set.

59 BASIC BIOLOGICAL SCIENCES↗