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Understanding the behavior of microbial consortia is crucial for predicting metabolite production by microorganisms. Genome-scale network reconstructions enable the computation of metabolic interactions and specific associations within microbial consortia underpinning the production of different metabolites. In the context of the human gut, butyrate is a central metabolite produced by bacteria that plays a key role within the gut microbiome impacting human health. Despite its importance, there is a lack of computational methods capable of predicting its production as a function of the consortium composition. Here, we present a novel machine-learning approach leveraging automatically generated genome-scale metabolic models to tackle this limitation. Briefly, all consortia made of two up to 13 members from a pool of 19 bacteria with known genomes, including at least one butyrate producer from a pool of three known producer species, were built and their (maximum) in silico butyrate production simulated. Using network-derived descriptors from each bacteria, butyrate production by the above consortia was used as training data for various machine learning models. The performance of the algorithms was evaluated using k-fold cross-validation and new experimental data, displaying a Pearson correlation coefficient exceeding 0.75 for the predicted and observed butyrate production in two bacteria consortia. While consortia with more than two bacteria showed generally worse predictions, the best machine-learning models still outperformed predictions from genome-scale metabolic models alone. Overall, this approach provides a valuable tool and framework for probing promising butyrate-producing consortia on a large scale, guiding experimentation, and more importantly, predicting metabolic production by consortia.

This article presents a numerical scheme for the variational model formulated by Calderer et al. [J. Elast., 141 (2020), pp. 51–73] for the debonding of a hydrogel film from a rigid substrate upon exposure to solvent, in the two-dimensional case of a film placed between two parallel walls. It builds upon the scheme introduced by Song et al. [J. Elast., 153 (2023), pp. 651–679] for completely bonded gels, which fails to be robust in the case of gels that are already debonded. The new scheme is used to compute the energy release rate function, based on which predictions are offered for the threshold thickness below which the gel/substrate system is stable against debonding. This study, in turn, makes it possible to validate a theoretical estimate for the energy release rate obtained in the cited works, which is based on a thin-film asymptotic analysis and which, due to its explicit nature, is potentially valuable in medical device development. An existence theorem and rigorous justifications of some approximations made in our numerical scheme are also provided.

In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error is equivalent to the sum of two residuals provided that the underlying variational formulation is well posed. The first contribution is the projection of the residual to a finite-dimensional space and is therefore computable, while the second one can be reliably estimated by a computable upper bound in many practical scenarios. Assuming sufficiently accurate quadrature, our findings can be used to estimate the error of, e.g., neural network outputs. Two important applications can be considered during optimization: first, the estimators are used to monitor the error in each solver step, or, second, the two estimators are included in the loss functional, and therefore provide control over the error. As a model problem, we consider a second-order elliptic partial differential equation and discuss different variational formulations thereof, including several options to include boundary conditions in the estimators. Various numerical experiments are presented to validate our findings.

Publisher: Mathematical Control and Related Fields, Link>

ABSTRACT

In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume the existence of an appropriate estimator, which has been established in the literature using voltage measurements. By applying backstepping and Lyapunov tools, we are able to build observers and to design output feedback controllers giving a positive answer to the SOC tracking problem. We provide convergence proofs and perform some numerical simulations to illustrate our theoretical results.

Resolving the details of an object from coarse-scale measurements is a classical problem in applied mathematics. This problem is usually formulated as extrapolating the Fourier transform of the object from a bounded region to the entire space, that is, in terms of performing extrapolation in frequency. This problem is ill-posed unless one assumes that the object has some additional structure. When the object is compactly supported, then it is well-known that its Fourier transform can be extended to the entire space. However, it is also well-known that this problem is severely ill-conditioned. In this work, we assume that the object is known to belong to a collection of compactly supported functions and, instead performing extrapolation in frequency to the entire space, we study the problem of extrapolating to a larger bounded set using dilations in frequency and a single Fourier multiplier. This is reminiscent of the refinement equation in multiresolution analysis. Under suitable conditions, we prove the existence of a worst-case optimal multiplier over the entire collection, and we show that all such multipliers share the same canonical structure. When the collection is finite, we show that any worst-case optimal multiplier can be represented in terms of an Hermitian matrix. This allows us to introduce a fixed-point iteration to find the optimal multiplier. This leads us to introduce a family of multipliers, which we call \Sigma-multipliers, that can be used to perform extrapolation in frequency. We establish connections between \Sigma-multipliers and multiresolution analysis. We conclude with some numerical experiments illustrating the practical consequences of our results.

This work proposes an r-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as those arising from self-adjoint elliptic problems. The objective of the NN optimization is to determine the mesh node locations. For simplicity in two-dimensional problems, these locations are assumed to form a tensor product structure. The method is designed to solve parametric partial differential equations (PDEs). For each PDE parameter instance, the optimal r-adapted mesh generated by the NN is then solved with a standard FEM. The construction of FEM matrices and load vectors is implemented such that their derivatives with respect to mesh node locations, required for NN training, can be efficiently computed using automatic differentiation. However, the linear equation solver does not need to be differentiable, enabling the use of efficient, readily available `out-of-the-box' solvers. Consequently, the proposed approach retains the robustness and reliability guarantees of the FEM for each parameter instance, while the NN optimization adaptively adjusts the mesh node locations. The method's performance is demonstrated on parametric Poisson problems using one- and two-dimensional tensor product meshes.

Machine learning is emerging as a valuable tool in mitigating and adapting to climate change, while climate change has been noted as a valuable area for inspiring cutting-edge algorithms in machine learning. This workshop is intended to form connections and foster cross-pollination between researchers in machine learning and experts in complementary climate-relevant fields, in addition to providing a forum for those in the machine learning community who wish to tackle climate change. This workshop distinguishes itself from previous editions of the popular ‘Tackling Climate Change with Machine Learning’ workshop series by focusing on a key challenge: questioning common machine learning assumptions in the context of climate impact. Specifically, we will concentrate on two questions that are very timely for the machine learning community: (i) the various climate-related benefits and costs of large vs small models, (ii) the design of effective benchmarks for climate-related applications.

"Chemical Shift Imaging (CSI) or Chemical Shift Encoded Magnetic Resonance Imaging (CSE-MRI) enables the quantification of different chemical species in the human body, and it is one of the most widely used imaging modalities used to quantify fat in the human body. Although there have been substantial improvements in the design of signal acquisition protocols and the development of a variety of methods for the recovery of parameters of interest from the measured signal, it is still challenging to obtain a consistent and reliable quantification over the entire field of view. In fact, there are still discrepancies in the quantities recovered by different methods, and each exhibits a different degree of sensitivity to acquisition parameters such as the choice of echo times. Some of these challenges have their origin in the signal model itself. In particular, it is non-linear, and there may be different sets of parameters of interest compatible with the measured signal. For this reason, a thorough analysis of this model may help mitigate some of the remaining challenges, and yield insight into novel acquisition protocols. In this work, we perform an analysis of the signal model underlying CSI, focusing on finding suitable conditions under which recovery of the parameters of interest is possible. We determine the sources of non-identifiability of the parameters, and we propose a reconstruction method based on smooth non-convex optimization under convex constraints that achieves exact local recovery under suitable conditions. A surprising result is that the concentrations of the chemical species in the sample may be identifiable even when other parameters are not. We present numerical results illustrating how our theoretical results may help develop novel acquisition techniques, and showing how our proposed recovery method yields results comparable to the state-of-the-art. "

In previous work, the authors proposed a model of swelling-induced debonding that combines the classical work by Flory and Rehner with the variational theory of fracture mechanics by Griffith. These works explore the synergy between theory, laboratory experiments and finite element simulations. We study the swelling of partially bonded, three-dimensional gels, drawing on previous studies of the analogous two-dimensional geometries with the gel confined between parallel walls that suppress swelling in the perpendicular direction. One main goal is the calculation of the energy release rate associated with debonding. Assuming an adhesive toughness that does not change with time, the energy release rate allows us to find the threshold thickness of the membrane above which the gel is unstable to debonding. We also present numerical strategies that allow us to approximate such a threshold thickness, avoiding the computationally taxing fully three dimensional calculations.

This paper presents the design and application of a fractional order asymptotic adaptive observer coupled to an adaptive controller for the robust operation of high-cell density cultures in fed-batch mode. The control goal is to maximize biomass productivity by controlling the culture’s estimated specific growth rate. Since the specific growth rate cannot be measured, a fractional order asymptotic adaptive observer is proposed, based on the equivalent integer order asymptotic observer proposed before. Simulations are performed to validate the observer and controller, under the assumption that the system is in the oxidative regime under aerobic conditions. Obtained results show that, in close loop operation, the fractional adaptive observer behaves better than the integer order observer in the presence of measurement noise. For fractional orders of the observer in the range α G [0.6,0.8], it was observed a 51.71% increase in biomass concentration, compared to the biomass obtained with the classic integer-order observer. Furthermore, the controlled system reaches very low ethanol concentrations (< 1 grams per liter), which is desirable in this process.