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Metadynamics, a member of the `flat histogram' class of advanced sampling algorithms, has been widely used in molecular simulations to drive the exploration of states separated by high free energy barriers and promote comprehensive sampling…
The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation. Recently, diffusion models such as BioEmu have emerged as powerful equilibrium samplers that…
Reconstructing an infinite-dimensional signal from a finite set of measurements is a fundamental problem in approximation theory and signal processing. While the generalized sampling (GS) framework provides a robust methodology for…
Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification…
Anomaly detection holds considerable industrial significance, especially in scenarios with limited anomalous data. Currently, reconstruction-based and unsupervised representation-based approaches are the primary focus. However, unsupervised…
Understanding protein conformational dynamics is essential for elucidating biological function but remains challenging due to the wide range of timescales and the complexity of collective motions. Enhanced sampling methods overcome…
In molecular dynamics simulations, rare events, such as protein folding, are typically studied using enhanced sampling techniques, most of which are based on the definition of a collective variable (CV) along which acceleration occurs.…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
This paper presents a novel compressed sensing (CS) approach to high dimensional wireless channel estimation by optimizing the input to a deep generative network. Channel estimation using generative networks relies on the assumption that…
Machine learning for the parameterization of subgrid-scale processes in climate models has been widely researched and adopted in a few models. A key challenge in developing data-driven parameterization schemes is how to properly represent…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
Computational fluid dynamics (CFD) is a valuable tool for personalised, non-invasive evaluation of hemodynamics in arteries, but its complexity and time-consuming nature prohibit large-scale use in practice. Recently, the use of deep…
The {\Lambda}CDM model has long served as a robust and predictive framework for cosmology, successfully explaining a wide range of observations, including the accelerated expansion of the Universe. However, discrepancies in cosmological…
Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…
The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation…
Representation (feature) space is an environment where data points are vectorized, distances are computed, patterns are characterized, and geometric structures are embedded. Extracting a good representation space is critical to address the…
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of…
To directly simulate rare events using atomistic molecular dynamics is a significant challenge in computational biophysics. Well-established enhanced-sampling techniques do exist to obtain the thermodynamic functions for such systems. But…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…