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Flow matching (FM) is increasingly used in scientific domains for time series generation and forecasting, where data often arise from underlying dynamical systems. However, it is not well-understood whether it learns transferable dynamical…

Riboswitches, structured elements in the untranslated regions of messenger RNAs, regulate gene expression by binding specific metabolites. We introduce a kinetic network model that describes the functions of riboswitches at the systems…

Machine learning has recently emerged as a powerful tool for generating new molecular and material structures. The success of state-of-the-art models stems from their ability to incorporate physical symmetries, such as translation,…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be…

Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…

We present flow matching for reaction coordinates (FMRC), a novel deep learning algorithm designed to identify optimal reaction coordinates (RC) in biomolecular reversible dynamics. FMRC is based on the mathematical principles of…

Molecular communication (MC) allows nanomachines to communicate and cooperate with each other in a fluid environment. The diffusion-based MC is popular but is easily constrained by the transmit distance due to the severe attenuation of…

Conditional Flow Matching (CFM), a simulation-free method for training continuous normalizing flows, provides an efficient alternative to diffusion models for key tasks like image and video generation. The performance of CFM in solving…

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently…

This paper introduces a novel framework for image quality transfer based on conditional flow matching (CFM). Unlike conventional generative models that rely on iterative sampling or adversarial objectives, CFM learns a continuous flow…

The so-called Mixed Feedback Loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical…

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential…

During mRNA translation, several ribosomes attach to the same mRNA molecule simultaneously translating it into a protein. This pipelining increases the protein production rate. A natural and important question is what ribosomal density…

We propose residual denoising diffusion models (RDDM), a novel dual diffusion process that decouples the traditional single denoising diffusion process into residual diffusion and noise diffusion. This dual diffusion framework expands the…

Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network…

Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and…

We describe a new class of systems exhibiting return point memory (RPM) that are different from those discussed before in the context of ferromagnets. We show numerically that one dimensional random Ising antiferromagnets have RPM, when…

Factorization machines (FM) are a popular model class to learn pairwise interactions by a low-rank approximation. Different from existing FM-based approaches which use a fixed rank for all features, this paper proposes a Rank-Aware FM…

In room acoustic environments, the Relative Transfer Functions (RTFs) are controlled by few underlying modes of variability. Accordingly, they are confined to a low-dimensional manifold. In this letter, we investigate a RTF inverse…