Presentation
An Adjoint Method for Differentiable Fluid Simulation on Flow Maps
DescriptionThis paper presents a novel adjoint solver for differentiable fluid simulation
based on bidirectional flow maps. Our key observation is that the forward
fluid solver and its corresponding backward, adjoint solver share the same
flow map, constructed during the forward simulation. In the forward pass,
this map transports fluid impulse variables from the initial frame to the
current frame to simulate vortical dynamics. In the backward pass, the
same map propagates adjoint variables from the current frame back to the
initial frame to compute gradients. This shared long-range map allows the
accuracy of gradient computation to benefit directly from improvements
in flow map construction. Building on this insight, we introduce a novel
adjoint solver that solves the adjoint equations directly on the flow map,
enabling long-range and accurate differentiation of incompressible flows
without differentiating intermediate numerical steps or storing intermediate
variables, as required in conventional adjoint methods. To further improve
efficiency, we propose a long-short time-sparse flow map representation for
evolving adjoint variables. Our approach has low memory usage, requiring
only 6.53GB of data at a resolution of 192^3 while preserving high accuracy in
tracking vorticity, enabling new differentiable simulation tasks that require
precise identification, prediction, and control of vortex dynamics
based on bidirectional flow maps. Our key observation is that the forward
fluid solver and its corresponding backward, adjoint solver share the same
flow map, constructed during the forward simulation. In the forward pass,
this map transports fluid impulse variables from the initial frame to the
current frame to simulate vortical dynamics. In the backward pass, the
same map propagates adjoint variables from the current frame back to the
initial frame to compute gradients. This shared long-range map allows the
accuracy of gradient computation to benefit directly from improvements
in flow map construction. Building on this insight, we introduce a novel
adjoint solver that solves the adjoint equations directly on the flow map,
enabling long-range and accurate differentiation of incompressible flows
without differentiating intermediate numerical steps or storing intermediate
variables, as required in conventional adjoint methods. To further improve
efficiency, we propose a long-short time-sparse flow map representation for
evolving adjoint variables. Our approach has low memory usage, requiring
only 6.53GB of data at a resolution of 192^3 while preserving high accuracy in
tracking vorticity, enabling new differentiable simulation tasks that require
precise identification, prediction, and control of vortex dynamics
Event Type
Technical Papers
TimeWednesday, 17 December 20252:04pm - 2:15pm HKT
LocationMeeting Room S426+S427, Level 4