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Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…

We address a three-tier data-driven approach to solve the inverse problem in complex systems modelling from spatio-temporal data produced by microscopic simulators using machine learning. In the first step, we exploit manifold learning and…

We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed…

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

This paper advocates the use of implicit surface representation in autoencoder-based self-supervised 3D representation learning. The most popular and accessible 3D representation, i.e., point clouds, involves discrete samples of the…

Machine learning (ML) has found broad applicability in quantum information science in topics as diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for…

This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…

This paper aims to improve the explainability of Autoencoder's (AE) predictions by proposing two explanation methods based on the mean and epistemic uncertainty of log-likelihood estimate, which naturally arise from the probabilistic…

We present an extension to masked autoencoders (MAE) which improves on the representations learnt by the model by explicitly encouraging the learning of higher scene-level features. We do this by: (i) the introduction of a perceptual…

We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions,…

Numerical simulations play a critical role in design and development of engineering products and processes. Traditional computational methods, such as CFD, can provide accurate predictions but are computationally expensive, particularly for…

In this work we address the problem of real-time dynamic MRI reconstruction. There are a handful of studies on this topic; these techniques are either based on compressed sensing or employ Kalman Filtering. These techniques cannot achieve…

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…

Software development has entered a new era where large language models (LLMs) now serve as general-purpose reasoning engines, enabling natural language interaction and transformative applications across diverse domains. This paradigm is now…

To meet the growing demand for smarter, faster, and more efficient embodied AI solutions, we introduce a novel Mixture-of-Expert (MoE) method that significantly boosts reasoning and learning efficiency for embodied autonomous systems.…

Constant-curvature Riemannian manifolds (CCMs) have been shown to be ideal embedding spaces in many application domains, as their non-Euclidean geometry can naturally account for some relevant properties of data, like hierarchy and…

Maximum likelihood estimation (MLE) is a well-known estimation method used in many robotic and computer vision applications. Under Gaussian assumption, the MLE converts to a nonlinear least squares (NLS) problem. Efficient solutions to NLS…

Machine Learning (ML), particularly deep learning, has seen vast advancements, leading to the rise of Machine Learning-Enabled Systems (MLS). However, numerous software engineering challenges persist in propelling these MLS into production,…

Numerical simulation of non-linear partial differential equations plays a crucial role in modeling physical science and engineering phenomena, such as weather, climate, and aerodynamics. Recent Machine Learning (ML) models trained on…

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Autoencoders (AE) are generative stochastic networks with these desired properties. We integrate a special type of…