Arne Elofsson

Ricardo Vinuesa, Paola Cinnella, Jean Rabault et al. · uw

As modern scientific instruments generate vast amounts of data and the volume of information in the scientific literature continues to grow, machine learning (ML) has become an essential tool for organising, analysing, and interpreting these complex datasets. This paper explores the transformative role of ML in accelerating breakthroughs across a range of scientific disciplines. By presenting key examples -- such as brain mapping and exoplanet detection -- we demonstrate how ML is reshaping scientific research. We also explore different scenarios where different levels of knowledge of the underlying phenomenon are available, identifying strategies to overcome limitations and unlock the full potential of ML. Despite its advances, the growing reliance on ML poses challenges for research applications and rigorous validation of discoveries. We argue that even with these challenges, ML is poised to disrupt traditional methodologies and advance the boundaries of knowledge by enabling researchers to tackle increasingly complex problems. Thus, the scientific community can move beyond the necessary traditional oversimplifications to embrace the full complexity of natural systems, ultimately paving the way for interdisciplinary breakthroughs and innovative solutions to humanity's most pressing challenges.

Christopher Iliffe Sprague, Arne Elofsson, Hossein Azizpour

In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective Lyapunov function. Despite this, connections between control theory and generative models in the literature are sparse, even though there are several machine learning applications with physically stable data points. In this paper, we focus on such data and a recent class of deep generative models called flow matching. We apply tools of stochastic stability for time-independent systems to flow matching models. In doing so, we characterize the space of flow matching models that are amenable to this treatment, as well as draw connections to other control theory principles. We demonstrate our theoretical results on two examples.

Christopher Iliffe Sprague, Arne Elofsson, Hossein Azizpour

Modeling complex systems that evolve toward equilibrium distributions is important in various physical applications, including molecular dynamics and robotic control. These systems often follow the stochastic gradient descent of an underlying energy function, converging to stationary distributions around energy minima. The local covariance of these distributions is shaped by the energy landscape's curvature, often resulting in anisotropic characteristics. While flow-based generative models have gained traction in generating samples from equilibrium distributions in such applications, they predominately employ isotropic conditional probability paths, limiting their ability to capture such covariance structures. In this paper, we introduce Hessian-Informed Flow Matching (HI-FM), a novel approach that integrates the Hessian of an energy function into conditional flows within the flow matching framework. This integration allows HI-FM to account for local curvature and anisotropic covariance structures. Our approach leverages the linearization theorem from dynamical systems and incorporates additional considerations such as time transformations and equivariance. Empirical evaluations on the MNIST and Lennard-Jones particles datasets demonstrate that HI-FM improves the likelihood of test samples.

Elodie Laine, Stephan Eismann, Arne Elofsson et al.

The potential of deep learning has been recognized in the protein structure prediction community for some time, and became indisputable after CASP13. In CASP14, deep learning has boosted the field to unanticipated levels reaching near-experimental accuracy. This success comes from advances transferred from other machine learning areas, as well as methods specifically designed to deal with protein sequences and structures, and their abstractions. Novel emerging approaches include (i) geometric learning, i.e. learning on representations such as graphs, 3D Voronoi tessellations, and point clouds; (ii) pre-trained protein language models leveraging attention; (iii) equivariant architectures preserving the symmetry of 3D space; (iv) use of large meta-genome databases; (v) combinations of protein representations; (vi) and finally truly end-to-end architectures, i.e. differentiable models starting from a sequence and returning a 3D structure. Here, we provide an overview and our opinion of the novel deep learning approaches developed in the last two years and widely used in CASP14.