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A Copula-based variational autoencoder for uncertainty quantification in inverse problems: application to damage identification in an offshore wind turbine
Authors:
Ana Fernandez-Navamuel,
Martin Alberto Diaz Viera,
Matteo Croci
Abstract:
Structural Health Monitoring of Floating Offshore Wind Turbines (FOWTs) is critical for ensuring operational safety and efficiency. However, identifying damage in components like mooring systems from limited sensor data poses a challenging inverse problem, often characterized by multimodal solutions where various damage states could explain the observed response. To overcome it, we propose a Varia…
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Structural Health Monitoring of Floating Offshore Wind Turbines (FOWTs) is critical for ensuring operational safety and efficiency. However, identifying damage in components like mooring systems from limited sensor data poses a challenging inverse problem, often characterized by multimodal solutions where various damage states could explain the observed response. To overcome it, we propose a Variational Autoencoder (VAE) architecture, where the encoder approximates the inverse operator, while the decoder approximates the forward. The posterior distribution of the latent space variables is probabilistically modeled, describing the uncertainties in the estimates. This work tackles the limitations of conventional Gaussian Mixtures used within VAEs, which can be either too restrictive or computationally prohibitive for high-dimensional spaces. We propose a novel Copula-based VAE architecture that decouples the marginal distribution of the variables from their dependence structure, offering a flexible method for representing complex, correlated posterior distributions. We provide a comprehensive comparison of three different approaches for approximating the posterior: a Gaussian Mixture with a diagonal covariance matrix, a Gaussian Mixture with a full covariance matrix, and a Gaussian Copula. Our analysis, conducted on a high-fidelity synthetic dataset, demonstrates that the Copula VAE offers a promising and tractable solution in high-dimensional spaces. Although the present work remains in the two-dimensional space, the results suggest efficient scalability to higher dimensions. It achieves superior performance with significantly fewer parameters than the Gaussian Mixture alternatives, whose parametrization grows prohibitively with the dimensionality. The results underscore the potential of Copula-based VAEs as a tool for uncertainty-aware damage identification in FOWT mooring systems.
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Submitted 11 January, 2026; v1 submitted 2 October, 2025;
originally announced October 2025.
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Analysis of the 2024 BraTS Meningioma Radiotherapy Planning Automated Segmentation Challenge
Authors:
Dominic LaBella,
Valeriia Abramova,
Mehdi Astaraki,
Andre Ferreira,
Zhifan Jiang,
Mason C. Cleveland,
Ramandeep Kang,
Uma M. Lal-Trehan Estrada,
Cansu Yalcin,
Rachika E. Hamadache,
Clara Lisazo,
Adrià Casamitjana,
Joaquim Salvi,
Arnau Oliver,
Xavier Lladó,
Iuliana Toma-Dasu,
Tiago Jesus,
Behrus Puladi,
Jens Kleesiek,
Victor Alves,
Jan Egger,
Daniel Capellán-Martín,
Abhijeet Parida,
Austin Tapp,
Xinyang Liu
, et al. (80 additional authors not shown)
Abstract:
The 2024 Brain Tumor Segmentation Meningioma Radiotherapy (BraTS-MEN-RT) challenge aimed to advance automated segmentation algorithms using the largest known multi-institutional dataset of 750 radiotherapy planning brain MRIs with expert-annotated target labels for patients with intact or postoperative meningioma that underwent either conventional external beam radiotherapy or stereotactic radiosu…
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The 2024 Brain Tumor Segmentation Meningioma Radiotherapy (BraTS-MEN-RT) challenge aimed to advance automated segmentation algorithms using the largest known multi-institutional dataset of 750 radiotherapy planning brain MRIs with expert-annotated target labels for patients with intact or postoperative meningioma that underwent either conventional external beam radiotherapy or stereotactic radiosurgery. Each case included a defaced 3D post-contrast T1-weighted radiotherapy planning MRI in its native acquisition space, accompanied by a single-label "target volume" representing the gross tumor volume (GTV) and any at-risk post-operative site. Target volume annotations adhered to established radiotherapy planning protocols, ensuring consistency across cases and institutions, and were approved by expert neuroradiologists and radiation oncologists. Six participating teams developed, containerized, and evaluated automated segmentation models using this comprehensive dataset. Team rankings were assessed using a modified lesion-wise Dice Similarity Coefficient (DSC) and 95% Hausdorff Distance (95HD). The best reported average lesion-wise DSC and 95HD was 0.815 and 26.92 mm, respectively. BraTS-MEN-RT is expected to significantly advance automated radiotherapy planning by enabling precise tumor segmentation and facilitating tailored treatment, ultimately improving patient outcomes. We describe the design and results from the BraTS-MEN-RT challenge.
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Submitted 21 July, 2025; v1 submitted 28 May, 2024;
originally announced May 2024.
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Zipping Strategies and Attribute Grammars
Authors:
José Nuno Macedo,
Marcos Viera,
João Saraiva
Abstract:
Strategic term rewriting and attribute grammars are two powerful programming techniques widely used in language engineering. The former, relies on strategies to apply term rewrite rules in defining language transformations, while the latter is suitable to express context-dependent language processing algorithms. Each of these techniques, however, is usually implemented by its own powerful and larg…
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Strategic term rewriting and attribute grammars are two powerful programming techniques widely used in language engineering. The former, relies on strategies to apply term rewrite rules in defining language transformations, while the latter is suitable to express context-dependent language processing algorithms. Each of these techniques, however, is usually implemented by its own powerful and large language processor system. As a result, it makes such systems harder to extend and to combine.
In this paper, we present the embedding of both strategic tree rewriting and attribute grammars in a zipper-based, purely functional setting. Zippers provide a simple, but generic tree-walk mechanism that is the building block technique we use to express the purely-functional embedding of both techniques. The embedding of the two techniques in the same setting has several advantages: First, we easily combine/zip attribute grammars and strategies, thus providing language engineers the best of the two worlds. Second, the combined embedding is easier to maintain and extend since it is written in a concise and uniform setting. This results in a very small library which is able to express advanced (static) analysis and transformation tasks. We show the expressive power of our library in optimizing Haskell let expressions, expressing several Haskell refactorings and solving several language processing tasks of the LDTA Tool Challenge.
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Submitted 20 October, 2021; v1 submitted 15 October, 2021;
originally announced October 2021.
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A Gradual Type System for Elixir
Authors:
Mauricio Cassola,
Agustín Talagorria,
Alberto Pardo,
Marcos Viera
Abstract:
Elixir is a functional programming language with dynamic typing. We propose a gradual type system that makes it possible to perform type-checking on a significant fragment of the language. An important feature of the type system is that it does not require any syntactic change to Elixir. Type information is provided by means of function signatures which are declared in terms of Elixir typespec dir…
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Elixir is a functional programming language with dynamic typing. We propose a gradual type system that makes it possible to perform type-checking on a significant fragment of the language. An important feature of the type system is that it does not require any syntactic change to Elixir. Type information is provided by means of function signatures which are declared in terms of Elixir typespec directives. The proposed type system is based on subtyping and is backward compatible, as it allows the presence of untyped code fragments. We have implemented a prototype of the type-checker in Elixir itself.
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Submitted 16 April, 2021;
originally announced April 2021.
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A Lazy Language Needs a Lazy Type System: Introducing Polymorphic Contexts
Authors:
S. Doaitse Swierstra,
Marcos Viera,
Atze Dijkstra
Abstract:
Most type systems that support polymorphic functions are based on a version of System-F. We argue that this limits useful programming paradigms for languages with lazy evaluation. We motivate an extension of System-F alleviating this limitation.
First, using a sequence of examples, we show that for lazily evaluated languages current type systems may force one to write a program in an unnatural w…
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Most type systems that support polymorphic functions are based on a version of System-F. We argue that this limits useful programming paradigms for languages with lazy evaluation. We motivate an extension of System-F alleviating this limitation.
First, using a sequence of examples, we show that for lazily evaluated languages current type systems may force one to write a program in an unnatural way; we in particular argue that in such languages the relationship between polymorphic and existential types can be made more systematic by allowing to pass back (part of) an existential result of a function call as an argument to the the function call that produced that value.
After presenting our extension to System-F we show how we can implement the strict-state thread monad $\mathrm{ST}$ by using a returned existential type in specialising the polymorphic function which returns that type. Currently this monad is built-in into the runtime system of GHC and as such has become part of the language.
Our proposed language extension, i.e. the introduction of polymorphic contexts, reverses the relationship between the context of a function call and the called function with respect to where it is decided with which type to instantiate a type variable.
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Submitted 14 December, 2016;
originally announced December 2016.