Gibbs Sampling Will Fail in Outlier Problems with Strong Masking

<p style='text-indent:20px;'>In this paper, we investigate the use of the Euler characteristic for the topological data analysis, particularly over higher dimensional parameter spaces. The Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, primarily in the context of random fields. The goal of this paper, is to present the extension of using the Euler characteristic in higher dimensional parameter spaces. The topological data analysis of higher dimensional parameter spaces using stronger invariants such as homology, has and continues to be the subject of intense research. However, as important theoretical and computational obstacles remain, the use of the Euler characteristic represents an important intermediary step toward multi-parameter topological data analysis. We show the usefulness of the techniques using generated examples as well as a real world dataset of detecting diabetic retinopathy in retinal images.</p>

Galaxy formation models within cosmological hydrodynamical simulations contain numerous parameters with nontrivial influences over the resulting properties of simulated cosmic structures and galaxy populations. It is computationally challenging to sample these high dimensional parameter spaces with simulations, in particular for halos in the high-mass end of the mass function. In this work, we develop a novel sampling and reduced variance regression method, CARPoolGP, which leverages built-in correlations between samples in different locations of high dimensional parameter spaces to provide an efficient way to explore parameter space and generate low-variance emulations of summary statistics. We use this method to extend the Cosmology and Astrophysics with machinE Learning Simulations to include a set of 768 zoom-in simulations of halos in the mass range of 1013–1014.5 M ⊙ h −1 that span a 28-dimensional parameter space in the IllustrisTNG model. With these simulations and the CARPoolGP emulation method, we explore parameter trends in the Compton Y–M, black hole mass–halo mass, and metallicity–mass relations, as well as thermodynamic profiles and quenched fractions of satellite galaxies. We use these emulations to provide a physical picture of the complex interplay between supernova and active galactic nuclei feedback. We then use emulations of the Y–M relation of massive halos to perform Fisher forecasts on astrophysical parameters for future Sunyaev–Zeldovich observations and find a significant improvement in forecasted constraints. We publicly release both the simulation suite and CARPoolGP software package.

We propose a method for optimizing control policies for assistive lower-limb devices. The method frames parameter selection as a dueling bandits problem in which a user indicates his or her qualitative preferences between pairs of parameter sets chosen from a library. We generate the library through an offline optimization procedure that seeks to reproduce the varied gaits of healthy human subjects. By separating the parameter selection process into online and offline portions, the method can handle high-dimensional parameter spaces and produces policies that can generalize to different gait scenarios such as speed variation. We evaluate the method on five subjects walking on a powered knee and ankle prosthesis governed by a neuromuscular control policy that has 43 parameters. We find the five subjects preferred four different parameter sets from the library and that the resulting optima resemble intact subject gait data. This result suggests the offline portion of the optimization method indeed produces control parameters that can adapt to different gaits. Moreover, we find that for three out of the four parameter sets we tested, the procedure also generates parameters that improve the ability of the prosthesis to adapt to increasing gait speed by increasing ankle net work production. The results encourage further research and exploration in clinical settings toward advanced prosthesis controls that employ online learning.

Obtaining the set of cosmological parameters consistent with observational data is an important exercise in current cosmological research. It involves finding the global maximum of the likelihood function in the multi-dimensional parameter space. Currently sampling based methods, which are in general stochastic in nature, like Markov-Chain Monte Carlo(MCMC), are being commonly used for parameter estimation. The beauty of stochastic methods is that the computational cost grows, at the most, linearly in place of exponentially (as in grid based approaches) with the dimensionality of the search space. MCMC methods sample the full joint probability distribution (posterior) from which one and two dimensional probability distributions, best fit (average) values of parameters and then error bars can be computed. In the present work we demonstrate the application of another stochastic method, named Particle Swarm Optimization (PSO), that is widely used in the field of engineering and artificial intelligence, for cosmological parameter estimation from WMAP seven years data. We find that there is a good agreement between the values of the best fit parameters obtained from PSO and publicly available code COSMOMC. However, there is a slight disagreement between error bars mainly due to the fact that errors are computed differently in PSO. Apart from presenting the results of our exercise, we also discuss the merits of PSO and explain its usefulness in more extensive search in higher dimensional parameter space.

In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem ill-defined: the model is consistent with the data for many values of its parameters. The objective is to find the probability distribution of parameter values consistent with the data, a problem that can be cast as the exploration of a high dimensional convex polytope. In this work we introduce a novel algorithm to solve this problem efficiently. It provides results that are statistically indistinguishable from currently used numerical techniques while its running time scales linearly with the system size. We show that the algorithm performs robustly in many abstract and practical applications. As working examples we simulate the effects of restricting reaction fluxes on the space of feasible phenotypes of a genome scale Escherichia coli metabolic network and infer the traffic flow between origin and destination nodes in a real communication network.

Reliable simulation of carbon and water fluxes in forest ecosystems is essential for understanding global energy, carbon, and water cycles, while it remains limited by the large number of poorly constrained parameters in land surface models, particularly in regions lacking flux observations. While model-data integration using satellite and eddy covariance data has improved performance, it does not resolve the fundamental problem of parameter identifiability.Here, we use SINDBAD (Koirala et al., 2025), a model-data integration framework, to evaluate whether eco evolutionary optimality (EEO) principles can act as effective constraints on a coupled carbon water land surface model when flux observations are unavailable. Using 37 forest sites worldwide spanning 1979-2017, we compare three experiments that differ in the type of constraints applied, i.e., vegetation structure only, vegetation structure plus flux observations, and vegetation structure plus EEO based constraints, to assess to what extent theoretical optimality principles can help even without direct flux information.We find that vegetation structure alone is insufficient to reproduce observed carbon and water fluxes, especially at water limited sites. Incorporating EEO constraints leads to clear improvements in simulations of gross primary productivity, ecosystem respiration, and evapotranspiration under water limitation, while effects are weaker at energy limited sites. EEO constrained simulations also show more realistic sensitivities of fluxes to precipitation and temperature, in some cases exceeding those obtained when flux observations are directly assimilated.These results suggest that eco evolutionary optimality principles can provide meaningful constraints on land surface models with high dimensional parameter spaces, reducing effective parameter uncertainty under data sparse conditions.

Model order reduction for large-scale structures with local nonlinearities

This paper focuses on the placement of cameras in order to achieve the highest possible localization accuracy with a multi-camera system. The cameras have redundant fields of view. They have to be placed according to some natural constraints but user defined constraints are allowed as well. A camera model is described and the components causing the localization errors are identified. Some localization accuracy measures are defined for any number of cameras. The multi-camera placement is analytically formulated using the expanded measures for multiple cameras. An example of placing two cameras is shown and the generalizations into higher dimensional parameter spaces are examined. There are publications where camera placement algorithms are formulated or compared. We make an attempt to examine the analytical solution of this problem in case of different objective functions.

Path planning plays a vital role in robot navigation and manipulation, and multiple types of algorithms have been introduced to address this problem. Rapidly-exploring Random Tree (RRT) based algorithms have many advantages over other path planning algorithms. For example, RRT is suitable to solve the path planning problem in high dimensional space and can easily handle robot differential constraints. Informed RRT* is a method that uses the prolate hyper-spheroid to speed up the optimization process, but its efficiency will decrease to the same level as RRT* when the hyper-spheroid covers most of the state space. To overcome this drawback, we further propose a Sliding-Window Informed RRT* (SWIRRT*), which combines the sliding-window thought into the Informed RRT*, taking the advantage of the initial path and make the path optimization much faster. Simulations in 2D space have been carried out to demonstrate that our proposed method can improve the RRT-like algorithm's convergence speed.

We consider scalar hyperbolic conservation laws in several space dimensions, with a class of random (and parametric) flux functions. We propose a Karhunen--Loève expansion on the state space of the random flux. For random flux functions which are continuously differentiable with respect to the state variable $u$, we prove the existence of a unique random entropy solution. Using a Karhunen--Loève spectral decomposition of the random flux into principal components with respect to the state variables, we introduce a family of parametric, deterministic entropy solutions on high-dimensional parameter spaces. We prove bounds on the sensitivity of the parametric and of the random entropy solutions on the Karhunen--Loève parameters. We also outline the convergence analysis for two classes of discretization schemes, the multilevel Monte Carlo finite volume method (MLMCFVM), developed in [S. Mishra and C. Schwab, Math. Comp., 81 (2012), pp. 1979--2018], [S. Mishra, C. Schwab, and J. Šukys, J. Comput. Phys., 231 (2012), pp. 3365--3388], and [S. Mishra, C. Schwab, and J. Šukys, Multi-level Monte Carlo finite volume methods for uncertainty quantification in nonlinear systems of balance laws, in Uncertainty Quantification in Computational Fluid Dynamics, Lecture Notes in Comput. Sci. Eng. 92, Springer, Heidelberg, 2013, pp. 225--294], and the stochastic collocation finite volume method (SCFVM) of [S. Tokareva, Stochastic Finite Volume Methods for Computational Uncertainty Quantification in Hyperbolic Conservation Laws, Ph.D. dissertation, ETH Diss. Nr. 21498, ETH Zürich, Zürich, Switzerland]. (A corrected version is attached.)

We consider parameter identification problems in parametrized partial differential equations (PDEs). These lead to nonlinear ill-posed inverse problems. One way of solving them is using iterative regularization methods, which typically require numerous amounts of forward solutions during the solution process. In this article we consider the nonlinear Landweber method and couple it with the reduced basis method as a model order reduction technique in order to reduce the overall computational time. In particular, we consider PDEs with a high-dimensional parameter space, which are known to pose difficulties in the context of reduced basis methods. We present a new method that is able to handle such high-dimensional parameter spaces by combining the nonlinear Landweber method with adaptive online reduced basis updates. It is then applied to the inverse problem of reconstructing the conductivity in the stationary heat equation.

Glycan structures account for up to 35% of the mass of cardiac sodium ( Nav ) channels. To question whether and how reduced sialylation affects Nav activity and cardiac electrical signaling, we conducted a series of in vitro experiments on ventricular apex myocytes under two different glycosylation conditions, reduced protein sialylation (ST3Gal4(-/-)) and full glycosylation (control). Although aberrant electrical signaling is observed in reduced sialylation, realizing a better understanding of mechanistic details of pathological variations in INa and AP is difficult without performing in silico studies. However, computer model of Nav channels and cardiac myocytes involves greater levels of complexity, e.g., high-dimensional parameter space, nonlinear and nonconvex equations. Traditional linear and nonlinear optimization methods have encountered many difficulties for model calibration. This paper presents a new statistical metamodeling approach for efficient computer experiments and optimization of Nav models. First, we utilize a fractional factorial design to identify control variables from the large set of model parameters, thereby reducing the dimensionality of parametric space. Further, we develop the Gaussian process model as a surrogate of expensive and time-consuming computer models and then identify the next best design point that yields the maximal probability of improvement. This process iterates until convergence, and the performance is evaluated and validated with real-world experimental data. Experimental results show the proposed algorithm achieves superior performance in modeling the kinetics of Nav channels under a variety of glycosylation conditions. As a result, in silico models provide a better understanding of glyco-altered mechanistic details in state transitions and distributions of Nav channels. Notably, ST3Gal4(-/-) myocytes are shown to have higher probabilities accumulated in intermediate inactivation during the repolarization and yield a shorter refractory period than WTs. The proposed statistical design of computer experiments is generally extensible to many other disciplines that involve large-scale and computationally expensive models.

This paper presents a coarse coding technique and an action selection scheme for reinforcement learning (RL) in multi-dimensional and continuous state-action spaces following conventional and sound RL manners. RL in high- dimensional continuous domains includes two issues: one is a generalization problem for value-function approximation, and the other is a sampling problem for action selection over multi-dimensional continuous action spaces. The proposed method combines random rectangular coarse coding with an action selection scheme using Gibbs-sampling. The random rectangular coarse coding is very simple and quite suited both to approximate Q-functions in high-dimensional spaces and to execute Gibbs sampling. Gibbs sampling enables us to execute action selection following Boltsmann distribution over high-dimensional action space.

The convergence and correctness of the UCT algorithm is a hot research problem. Previous research has shown the convergence of UCT-based algorithm on simultaneous turns or random turns games, but little is known for traditional alternating turns games. In this paper, we analyze the performance of the UCT algorithm in a 2-player imperfect information alternating turns game, 2 × 4 Chinese dark chess (CDC). The performance of the UCT algorithm is measured by the correctness rate and convergence speed. The correctness is defined by the percentage that the UCT algorithm outputs the same move with the one having the best game theoretic value. The convergence speed is defined by the entropy of a set of moves, which are output by the UCT algorithm using the same number of iterations. Experimental result shows the convergence of the UCT algorithm in the CDC, which can also be applied to explain the existence of diminishing returns in the UCT algorithm. Experimental result also shows an UCT algorithm does not always output moves with the best game theoretic value, but these with the highest chance of winning.

Water-alternating-gas (WAG) injection is a gas-based enhanced oil recovery (EOR) technique used to overcome problems related with gas injection including gravity override, viscous fingering, and channeling. The WAG EOR technique is used to control gas mobility, which boosts project economics. Water alternating gas (WAG) has the dual benefit of higher recovery than continuous gas injection and CO2 sequestration. Higher sweep efficiencies and conformance control have been shown to increase the life cycle net present value (NPV) for improved field development and deployment planning. Nevertheless, a poor WAG design often results in unfavorable oil recovery. This study investigates WAG optimization in a sandstone field using a hybrid numerical-machine learning (ML) model. In this work, we present a hybrid neural approach for optimizing the WAG injection process that can be easily integrated as a workflow with any existing reservoir simulator for optimal WAG parameters to maximize reservoir life cycle cumulative recoveries. The reservoir simulator is treated as a sample generator to form an ensemble of recovery scenarios with the WAG parameters as inputs to a dense neural network (DNN) and outputs/labels as cumulative recoveries. The neural network then serves two roles: 1) a readily available map between WAG parameters and cumulative recoveries for reduced computational cost and hence faster on-demand evaluation, and 2) as a repository condensing important correlations that can be appended with additional samples or reduced by removing redundant samples (simulation runs). Consequently, the hybrid neural approach also provides a clear picture of which simulation runs (or samples) are more conducive to optimal recovery predictions for an effective strategy to sample the high dimensional WAG parameter space and reduced compute times. This becomes especially important when we consider field scale optimization scenarios with multiple wells each with their separate injection schedules requiring exponentially increasing samples with a brute force ensemble approach (add an example in the introduction section or later and cross-refer here).