title: Meta Flow Matching: Integrating Vector Fields on the Wasserstein
    Manifold
summary: 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 for predicting the temporal evolution of populations
  across novel samples and unseen environments. Flow-based models allow for
  learning these dynamics at the population level - they model the evolution of
  the entire distribution of samples. However, current flow-based models are
  limited to a single initial population and a set of predefined conditions which
  describe different dynamics. We argue that multiple processes in natural
  sciences have to be represented as vector fields on the Wasserstein manifold of
  probability densities. That is, the change of the population at any moment in
  time depends on the population itself due to the interactions between samples.
  In particular, this is crucial for personalized medicine where the development
  of diseases and their respective treatment response depends on the
  microenvironment of cells specific to each patient. We propose Meta Flow
  Matching (MFM), a practical approach to integrating along these vector fields
  on the Wasserstein manifold by amortizing the flow model over the initial
  populations. Namely, we embed the population of samples using a Graph Neural
  Network (GNN) and use these embeddings to train a Flow Matching model. This
  gives MFM the ability to generalize over the initial distributions unlike
  previously proposed methods. We demonstrate the ability of MFM to improve
  prediction of individual treatment responses on a large scale multi-patient
  single-cell drug screen dataset.
paper_authors._id: 66d205cf3b8f08e1b22658b6
paper_authors.name: Lazar Atanackovic
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-09-02T07:17:45.966Z
paper_authors._id: 66cd0e523f6dbc62985b184b
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/66cd0e523f6dbc62985b184b/vlHTY9LKJ0jKeAniHdGil.jpeg
paper_authors.fullname: Lazar Atanackovic
paper_authors.type: user
paper_authors.user: lazaratan
paper_authors._id: 66d205cf3b8f08e1b22658b7
paper_authors.name: Xi Zhang
paper_authors._id: 66d205cf3b8f08e1b22658b8
paper_authors.name: Brandon Amos
paper_authors._id: 66d205cf3b8f08e1b22658b9
paper_authors.name: Mathieu Blanchette
paper_authors._id: 66d205cf3b8f08e1b22658ba
paper_authors.name: Leo J. Lee
paper_authors._id: 66d205cf3b8f08e1b22658bb
paper_authors.name: Yoshua Bengio
paper_authors._id: 66d205cf3b8f08e1b22658bc
paper_authors.name: Alexander Tong
paper_authors._id: 66d205cf3b8f08e1b22658bd
paper_authors.name: Kirill Neklyudov
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-09-02T07:17:48.052Z
paper_authors._id: 65039d7a93574a897179139a
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/65039d7a93574a897179139a/szQAWkF2M9XnYKykmX8Cg.jpeg
paper_authors.fullname: Kirill Neklyudov
paper_authors.type: user
paper_authors.user: necludov
paper_title: Meta Flow Matching: Integrating Vector Fields on the Wasserstein
    Manifold
paper_summary: 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 for predicting the temporal evolution of populations
  across novel samples and unseen environments. Flow-based models allow for
  learning these dynamics at the population level - they model the evolution of
  the entire distribution of samples. However, current flow-based models are
  limited to a single initial population and a set of predefined conditions which
  describe different dynamics. We argue that multiple processes in natural
  sciences have to be represented as vector fields on the Wasserstein manifold of
  probability densities. That is, the change of the population at any moment in
  time depends on the population itself due to the interactions between samples.
  In particular, this is crucial for personalized medicine where the development
  of diseases and their respective treatment response depends on the
  microenvironment of cells specific to each patient. We propose Meta Flow
  Matching (MFM), a practical approach to integrating along these vector fields
  on the Wasserstein manifold by amortizing the flow model over the initial
  populations. Namely, we embed the population of samples using a Graph Neural
  Network (GNN) and use these embeddings to train a Flow Matching model. This
  gives MFM the ability to generalize over the initial distributions unlike
  previously proposed methods. We demonstrate the ability of MFM to improve
  prediction of individual treatment responses on a large scale multi-patient
  single-cell drug screen dataset.
paper_ai_keywords: flow-based models Wasserstein manifold probability densities vector fields Graph Neural Network (GNN) Flow Matching personalized medicine single-cell drug screen treatment responses