Designing civil structures such as bridges, dams or buildings is a complex task requiring many synergies from several experts. Each is responsible for different parts of the process. This is often done in a sequential manner, e.g. the structural engineer makes a design under the assumption of certain material properties (e.g. the strength class of the concrete), and then the material engineer optimizes the material with these restrictions. This paper proposes a holistic optimization procedure, which combines the concrete mixture design and structural simulations in a joint, forward workflow that we ultimately seek to invert. In this manner, new mixtures beyond standard ranges can be considered. Any design effort should account for the presence of uncertainties which can be aleatoric or epistemic as when data is used to calibrate physical models or identify models that fill missing links in the workflow. Inverting the causal relations established poses several challenges especially when these involve physics-based models which most often than not do not provide derivatives/sensitivities or when design constraints are present. To this end, we advocate Variational Optimization, with proposed extensions and appropriately chosen heuristics to overcome the aforementioned challenges. The proposed methodology is illustrated using the design of a precast concrete beam with the objective to minimize the global warming potential while satisfying a number of constraints associated with its load-bearing capacity after 28days according to the Eurocode, the demoulding time as computed by a complex nonlinear Finite Element model, and the maximum temperature during the hydration.
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We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.
Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some problems, this simulation is infeasible, leading to the discretization of state variable space and the need to train one neural network for each data point. This approach becomes computationally inefficient when dealing with large state variable spaces. In this paper, we consider a class of this type of stochastic optimal control problems and introduce an effective solution employing multitask neural networks. To train our multitask neural network, we introduce a novel scheme that dynamically balances the learning across tasks. Through numerical experiments on real-world derivatives pricing problems, we prove that our method outperforms state-of-the-art approaches.
In the symbolic verification of cryptographic protocols, a central problem is deciding whether a protocol admits an execution which leaks a designated secret to the malicious intruder. Rusinowitch & Turuani (2003) show that, when considering finitely many sessions, this ``insecurity problem'' is NP-complete. Central to their proof strategy is the observation that any execution of a protocol can be simulated by one where the intruder only communicates terms of bounded size. However, when we consider models where, in addition to terms, one can also communicate logical statements about terms, the analysis of the insecurity problem becomes tricky when both these inference systems are considered together. In this paper we consider the insecurity problem for protocols with logical statements that include {\em equality on terms} and {\em existential quantification}. Witnesses for existential quantifiers may be unbounded, and obtaining small witness terms while maintaining equality proofs complicates the analysis considerably. We extend techniques from Rusinowitch & Turuani (2003) to show that this problem is also in NP.
The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce analogues for e-values of three popular nonparametric tests, define an analogue for e-values of Pitman's asymptotic relative efficiency, and apply it to the three nonparametric tests. We discuss limitations of our simple definition of asymptotic relative efficiency and list directions of further research.
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a single-index structure, while the other is included linearly through the high-dimensional vector formed by its discretised observations. For this model, two new algorithms are presented for selecting relevant variables in the linear part and estimating the model. Both procedures utilise the functional origin of linear covariates. Finite sample experiments demonstrated the scope of application of both algorithms: the first method is a fast algorithm that provides a solution (without loss in predictive ability) for the significant computational time required by standard variable selection methods for estimating this model, and the second algorithm completes the set of relevant linear covariates provided by the first, thus improving its predictive efficiency. Some asymptotic results theoretically support both procedures. A real data application demonstrated the applicability of the presented methodology from a predictive perspective in terms of the interpretability of outputs and low computational cost.
This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with semiparametrics, is proposed. A wide scope of asymptotic results is provided: this covers as well rates of convergence of the estimators as asymptotic behaviour of the variable selection procedure. Practical issues are analysed through finite sample simulated experiments while an application to Tecator's data illustrates the usefulness of our methodology.
There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a unified understanding of what the consequences of higher-order synergies and redundancies are for systems. Typical research treat the presence (or absence) of synergistic information as a dependent variable and report changes in the level of synergy in response to some change in the system. Here, we attempt to flip the script: rather than treating higher-order information as a dependent variable, we use evolutionary optimization to evolve boolean networks with significant higher-order redundancies, synergies, or statistical complexity. We then analyse these evolved populations of networks using established tools for characterizing discrete dynamics: the number of attractors, average transient length, and Derrida coefficient. We also assess the capacity of the systems to integrate information. We find that high-synergy systems are unstable and chaotic, but with a high capacity to integrate information. In contrast, evolved redundant systems are extremely stable, but have negligible capacity to integrate information. Finally, the complex systems that balance integration and segregation (known as Tononi-Sporns-Edelman complexity) show features of both chaosticity and stability, with a greater capacity to integrate information than the redundant systems while being more stable than the random and synergistic systems. We conclude that there may be a fundamental trade-off between the robustness of a systems dynamics and its capacity to integrate information (which inherently requires flexibility and sensitivity), and that certain kinds of complexity naturally balance this trade-off.
Inequality measures are quantitative measures that take values in the unit interval, with a zero value characterizing perfect equality. Although originally proposed to measure economic inequalities, they can be applied to several other situations, in which one is interested in the mutual variability between a set of observations, rather than in their deviations from the mean. While unidimensional measures of inequality, such as the Gini index, are widely known and employed, multidimensional measures, such as Lorenz Zonoids, are difficult to interpret and computationally expensive and, for these reasons, are not much well known. To overcome the problem, in this paper we propose a new scaling invariant multidimensional inequality index, based on the Fourier transform, which exhibits a number of interesting properties, and whose application to the multidimensional case is rather straightforward to calculate and interpret.
Asymptotic analysis for related inference problems often involves similar steps and proofs. These intermediate results could be shared across problems if each of them is made self-contained and easily identified. However, asymptotic analysis using Taylor expansions is limited for result borrowing because it is a step-to-step procedural approach. This article introduces EEsy, a modular system for estimating finite and infinitely dimensional parameters in related inference problems. It is based on the infinite-dimensional Z-estimation theorem, Donsker and Glivenko-Cantelli preservation theorems, and weight calibration techniques. This article identifies the systematic nature of these tools and consolidates them into one system containing several modules, which can be built, shared, and extended in a modular manner. This change to the structure of method development allows related methods to be developed in parallel and complex problems to be solved collaboratively, expediting the development of new analytical methods. This article considers four related inference problems -- estimating parameters with random sampling, two-phase sampling, auxiliary information incorporation, and model misspecification. We illustrate this modular approach by systematically developing 9 parameter estimators and 18 variance estimators for the four related inference problems regarding semi-parametric additive hazards models. Simulation studies show the obtained asymptotic results for these 27 estimators are valid. In the end, I describe how this system can simplify the use of empirical process theory, a powerful but challenging tool to be adopted by the broad community of methods developers. I discuss challenges and the extension of this system to other inference problems.
The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that can act as a basis for the system. In this paper, we demonstrate on real world data how the Augmented SINDy algorithm outperforms SINDy in the presence of system variable uncertainty. We then show SINDy can be further augmented to perform robustly when both kinds of uncertainty are present.
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