A5089119201- Model Reduction and Neural Networks
- Probabilistic and Robust Engineering Design
- Numerical methods for differential equations
- Advanced Numerical Methods in Computational Mathematics
- Genetic Associations and Epidemiology
- Radiomics and Machine Learning in Medical Imaging
- Molecular Biology Techniques and Applications
- Real-time simulation and control systems
- Advanced Numerical Analysis Techniques
- Prostate Cancer Diagnosis and Treatment
- Medical Imaging Techniques and Applications
- Advanced Radiotherapy Techniques
- Nuclear reactor physics and engineering
- Fluid Dynamics and Turbulent Flows
- Neural Networks and Applications
- Data Mining Algorithms and Applications
- Effects of Radiation Exposure
- Imbalanced Data Classification Techniques
- Numerical methods in engineering
- Electromagnetic Simulation and Numerical Methods
- Biomedical Text Mining and Ontologies
- Magnetic Properties and Applications
- Control Systems and Identification
- BRCA gene mutations in cancer
- Natural Language Processing Techniques
Politecnico di Milano
2020-2024
Abstract POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality reduction obtained through proper orthogonal decomposition (POD) the sake of efficiency, (ii) autoencoder architecture that further reduces POD space handful latent coordinates, (iii) dense neural network learn map describes dynamics coordinates...
Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for efficient approximation parameter-to-solution map. The research is motivated by limitations and drawbacks state-of-the-art algorithms, such as Reduced Basis method, when addressing problems that show slow decay in Kolmogorov n-width. Our work use deep autoencoders, which employ encoding decoding high fidelity solution manifold. To provide guidelines design consider nonlinear...
Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available literature still lack a rigorous justification on mathematical foundations. Motivated by this fact, paper we derive error bounds for approximation nonlinear operators means CNN models. More precisely, address case which an operator maps finite dimensional input μ∈Rp onto...
Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales their data. However, these numerical solutions are often computationally expensive due to the need capture fine details at small scales. As a result, simulating such phenomena becomes unaffordable for many-query applications, as parametrized systems scale-dependent features. Traditional projection-based reduced order models (ROMs) fail resolve issues, even...
Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution to parametrized time-dependent nonlinear partial differential equations (PDEs). In this context, full order models (FOMs), such as those relying on finite element method, can reach high levels of accuracy, however often yielding intensive run. For reason, surrogate are developed replace computationally expensive solvers with more...
Abstract Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the of mathematical operators. In present work, we introduce Mesh-Informed (MINNs), class architectures specifically tailored handle mesh based functional data, thus particular interest reduced order modeling parametrized Partial Differential Equations (PDEs). The driving idea behind MINNs is embed hidden layers into discrete spaces...
Background REQUITE (validating pREdictive models and biomarkers of radiotherapy toxicity to reduce side effects improve QUalITy lifE in cancer survivors) is an international prospective cohort study. The purpose this project was analyse a patients recruited into using deep learning algorithm identify patient-specific features associated with the development toxicity, test approach by attempting validate previously published genetic risk factors. Methods study involved prostate treated...
Within the framework of precision medicine, stratification individual genetic susceptibility based on inherited DNA variation has paramount relevance. However, one most relevant pitfalls traditional Polygenic Risk Scores (PRS) approaches is their inability to model complex high-order non-linear SNP-SNP interactions and effect phenotype (e.g. epistasis). Indeed, they incur in a computational challenge as number possible grows exponentially with SNPs considered, affecting statistical...
Abstract Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it exploited as powerful tool tackling complex problems which classical methods might fail. In this respect, deep autoencoders play fundamental role, they provide an extremely flexible reducing dimensionality given problem by leveraging nonlinear capabilities neural networks. Indeed, starting from paradigm, several successful approaches have...
In recent years, deep learning has gained increasing popularity in the fields of Partial Differential Equations (PDEs) and Reduced Order Modeling (ROM), providing domain practitioners with new powerful data-driven techniques such as Physics-Informed Neural Networks (PINNs), Operators, Deep Operator (DeepONets) Deep-Learning based ROMs (DL-ROMs). this context, autoencoders on Convolutional (CNNs) have proven extremely effective, outperforming established techniques, reduced basis method, when...
Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires significant number of model evaluations. The objective this work to mitigate the computational cost UQ 3D-1D multiscale microcirculation. To purpose, we present deep learning enhanced multi-fidelity Monte Carlo (DL-MFMC) method integrates information full-order (FOM) with coming from non-intrusive projection-based reduced order (ROM). latter constructed by leveraging on proper...
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction neural network model that approximates solution manifold through continuously adaptive local basis. In contrast to global methods, such as Principal (POD), adaptivity allows DOD overcome Kolmogorov barrier, making applicable wide spectrum parametric...
Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires significant number of model evaluations. The objective this work to mitigate the computational cost UQ 3D-1D multiscale microcirculation. To purpose, we present deep learning enhanced multi-fidelity Monte Carlo (DL-MFMC) method integrates information full-order (FOM) with coming from non-intrusive projection-based reduced order (ROM). latter constructed by leveraging on proper...
We consider a mixed formulation of parametrized elasticity problems in terms stress, displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce conservation linear angular momentum. Due the saddle-point structure, resulting system is computationally demanding solve directly, we therefore propose an efficient solution strategy based on decomposition stress variable. First, triangular solved obtain field that balances body boundary forces. Second, trained...
We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems which the constraint is given by mass conservation. Our approach employs classical neural network architectures and supervised learning, but it constructed such way that resulting Reduced Order Model (ROM) guaranteed to satisfy constraints exactly. The procedure based on splitting of PDE solution into satisfying homogenous...
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality reduction obtained through proper orthogonal decomposition (POD) the sake of efficiency, (ii) autoencoder architecture that further reduces POD space handful latent coordinates, (iii) dense neural network learn map describes dynamics coordinates function input...
Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In this context, full order models (FOMs), such as those relying on finite element method, can reach high levels accuracy, however often yielding intensive to run. For reason, surrogate are developed replace computationally expensive solvers with more...
Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales their data. However, these numerical solutions are often computationally expensive due to the need capture fine details at small scales. As a result, simulating such phenomena becomes unaffordable for many-query applications, as parametrized systems scale-dependent features. Traditional projection-based reduced order models (ROMs) fail resolve issues, even...