Deep learning predicts adhesive forces in soft viscoelastic contacts quickly and accurately.
problem Predicting the full time-resolved force trajectory of adhesive soft viscoelastic contacts is computationally expensive and impractical.
method Trained a deep learning model to predict the full force evolution from a prescribed displacement history, using FMS representation and various architectures.
result Best-performing model predicts complete force trajectory with low error metrics and fast inference time.
We show that the twisted Kähler-Ricci flow on a complex manifold X converges to a flow of moving free boundaries, in a certain scaling limit. This leads to a new phenomenon of singularity formation and topology change which can be seen as a complex generalization of the extensively studied formation of shocks in Hamilt…
New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.
problem Lack of reference atomistic forces makes force matching infeasible for MLCG force fields.
method Introduces noise-based kernels adapted to low-data regimes using normalizing flows.
result Flow-based kernels reduce local distortions while preserving global accuracy.
New algorithm efficiently trains machine learning models to atomic forces data.
problem Efficiently training machine learning models to large amounts of force data.
method Developed an efficient algorithm for training machine learning models to all available force data.
result Training to all available force data is only a few times more expensive than training to energies alone.
The paper integrates dissipative and curl forces using geometric methods.
problem Incorporating dissipative forces into curl forces for non-conservative systems.
method Geometric metriplectic approach, Herglotz principle, generalized Euler-Lagrange equation, Galley's method.
result Natural formulations for Lagrangian and Hamiltonian dynamics of non-conservative systems.
Improved CG force-field learning from all-atom data.
problem Training accurate coarse-grained models from all-atom simulations is challenging.
method Optimized force mapping to improve statistical efficiency of force-field learning.
result Substantially improved CG force-fields can be learned from the same simulation data.
Solves Plateau-Douglas problem for singular configurations in general metric spaces.
problem Existence of minimal surfaces for singular configurations.
method Generalized approach via minimal sequences in metric spaces.
result Existence of minimal surfaces for singular configurations in general metric spaces.
Paper introduces a PDE-free method for decomposing forces in any dimension.
problem Analyzing non-conservative forces in arbitrary dimensions.
method Geometric decomposition using homotopy operator and Frobenius theorem.
result Decomposes forces into gradient and antiexact components, characterizing curl forces.
Proposes linking energy and force uncertainty in deep learning potentials.
problem Uncertainty in predicted energies and forces in machine learning models.
method Introduces a spatially correlated noise process to link energy and force uncertainty.
result Demonstrates the approach on molecular datasets, linking energy and force uncertainties.
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study symmetries in the systems with gyroscopic forces to find out when these systems admi…
The paper analyzes errors in mechanical systems with external forces.
problem Error analysis of mechanical systems with external forces.
method Analysis of variational integrators with contact order r for discrete mechanical systems. result The contact order of the integrator is the same as the contact order of the original systems.
Study curve flows with global forcing terms using a distance comparison principle.
problem Analyse the behavior of curves under curve flows with global forcing terms.
method Prove a distance comparison principle for curve shortening flow with arbitrary global forcing terms.
result Established a distance comparison principle for curve flows with global forcing terms.
In this paper we provide a variational derivation of the Euler-Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others. Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the…
An important task in structural design is to quantify the structural performance of an object under the external forces it may experience during its use. The problem proves to be computationally very challenging as the external forces' contact locations and magnitudes may exhibit significant variations. We present an e…
We show that under suitable non-degeneracy conditions, complete gradient flow lines of the scalar curvature functional of a riemannian manifold perturb into eternal forced mean curvature flows with large forcing term.
The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.
problem Determining planar curves for constant-speed motion under specific force conditions.
method Analyzing the motion of a particle under friction and a central force field.
result Every solution to the constant-speed motion problem approaches either a circle or a logarithmic spiral.
The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network's own one-step-ahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of th…
Proposes a new model to price options considering market forces beyond Black-Scholes.
problem Tackles the limitations of the Black-Scholes model in capturing unexpected market behaviors.
method Uses the analogy between quantum harmonic oscillator and financial market dynamics to propose a new market force-driven model.
result Shows how various market forces can be incorporated to modify option pricing, providing practical applications.
Proves uniqueness of blowups for forced mean curvature flow.
problem Proving uniqueness of blowups for forced mean curvature flow.
method Adapting methods from Euclidean space mean curvature flow to handle forcing term and blow-up limits.
result Uniqueness of tangent cones for forced mean curvature flow at self-shrinkers and cylindrical self-shrinkers.
The paper simplifies complex mechanical systems with external forces.
problem Analyzing symmetric discrete mechanical systems with external forces.
method Lagrangian reduction and reconstruction for principal bundles.
result Evolution of momentum maps and Poisson structures under different conditions.
New insights into Hessian structure of neural networks reveal two forces.
problem Understanding the Hessian structure of neural networks.
method Analyzing the static and dynamic forces, comparing limit distributions using random matrix theory.
result The Hessian structure arises from a combination of static and dynamic forces, with C being a primary driver. We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…
In this paper, we consider the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. We show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all times and expand to infinity if the forcing term is large enough. The flow can also conver…
Study compares employers with and without anticipating strategic labor force responses.
problem Understanding and optimizing strategic interactions in labor markets.
method Formulation of causal strategic classification, theory, and experiments.
result Performatively optimal hiring policies improve employer and labor outcomes, but can also harm labor force utility.
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley [2013], Galley, Tsang, and Stein [2014]. We show that this construction is useful to…
The paper explains emergent phenomena in deep learning using entropic forces.
problem Understanding the cause of emergent phenomena in deep learning and large language models.
method Proposes a rigorous entropic-force theory for neural networks trained with SGD and variants.
result Shows that representation learning is governed by emergent entropic forces that break continuous symmetries and preserve discrete ones.
In this paper we study the blow up sequence of mean curvature flow of surfaces in R3 with additional forces. We prove that the blow up limit of a mean curvature flow of smoothly embedded surfaces with additional forces with finite entropy is a smoothly embedded self-shrinker.
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is …
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
problem Identification of nonlinear dynamic systems in engineering.
method Modeling the nonlinear restoring force as a Gaussian process, converting it to a state-space model, and inferring internal states and the nonlinear restoring force through filtering and smoothing.
result The approach effectively identifies nonlinear restoring forces in both simulated and experimental datasets.
The forcing relation of braids has been introduced for a 2-dimensional analogue of the Sharkovskii order on periods for maps of the interval. In this paper, by making use of the Nielsen fixed point theory and a representation of braid groups, we deduce a trace formula for the computation of the forcing order.
We develop variational integrators from discrete Hamiltonian systems with external forces.
problem Creating accurate discrete models of continuous Hamiltonian systems.
method Constructing discrete Hamiltonian systems with external forces, analyzing symplectic structure, and combining methods to build variational integrators.
result We derive variational integrators that approximate continuous Hamiltonian systems with high accuracy.
Curve shortening flow shrinks curves to points under certain conditions.
problem Understanding how curves shrink under curve shortening flow with ambient forces.
method Rescaling and curvature bounds analysis following Gage and Hamilton.
result Curves shrink to round points under certain curvature conditions.
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…
Study bi-harmonic flow with forcing term on smooth curves.
problem Analyzing the evolution of smooth, closed planar curves under bi-harmonic flow with a forcing term.
method Reformulated geometric flow using support function, scalar PDE characterization, Monge Ampére structure analysis.
result Convexity is preserved and steady-state solutions converge over long times under specific conditions.
CAMEL embeds data into a manifold using curvature-augmented forces.
problem Data visualization and dimensionality reduction.
method Formulates DR as a physics model with curvature-augmented forces.
result CAMEL outperforms existing methods on benchmark datasets.
Study physical work done by isotropic vector forces along isotropic curves.
problem Investigate physical work done by isotropic vector forces.
method Analyze forces represented by isotropic vectors acting along isotropic curves on a manifold with specific metric structures.
result Calculate the work done by isotropic vector forces along isotropic curves.
We consider embedded, smooth curves in the plane which are either closed or asymptotic to two lines. We study their behaviour under curve shortening flow with a global forcing term. Firstly, we prove an analogue to Huisken's distance comparison principle for curve shortening flow for initial curves whose local total cu…
Weibull weight-scale parameter λ evolves during AdamW training, with alignment, injection, and decay forces driving its growth and relaxation.
problem Understanding the evolution of the Weibull weight-scale parameter λ during AdamW training. method Deriving a leading-order three-force decomposition of the squared weight norm from AdamW updates.
result The alignment force dominates the rise phase, contributing 88-94% of the absolute force budget across four random seeds.
Study active nematic forces on curved surfaces, revealing new coupling mechanisms.
problem Understanding active nematic forces on curved surfaces.
method Developed a thermodynamically consistent surface model with nematic activity, analyzed topological defects.
result Active defects contribute both tangential and normal forces on curved surfaces.
We study perturbations of the Allen-Cahn equation and prove the convergence to forced mean curvature flow in the sharp interface limit. We allow for perturbations that are square-integrable with respect to the diffuse surface area measure. We give a suitable generalized formulation for forced mean curvature flow and ap…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form of flows of a given geodesic curvature is proposed. For illustration, the proble…
Study preserves symplectic structure in forced discrete mechanical systems.
problem Preserving symplectic structure in forced discrete mechanical systems.
method Analyzes a specific type of forced discrete mechanical system (Q,Ld,fd), preserving a symplectic structure on QimesQ. result The preserved symplectic structure can be seen as Marsden-Weinstein reduction of the canonical symplectic structure.
Machine learning generates coarse-grained force fields for molecular dynamics.
problem Creating thermodynamically consistent coarse-grained models for larger systems.
method Hybrid architecture using graph neural networks to learn molecular features.
result Framework reproduces thermodynamics for small biomolecular systems.
New strategies avoid forced exploration for unimodal bandits.
problem Optimal exploration of unimodal bandit problems.
method Adapting IMED strategy to unimodal structure without forced exploration.
result Proven optimal strategies for unimodal bandits.
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model complexity, or a full specification is hard to motivate. Latent force models achieve …
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when …
In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a long-time smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the extern…
Global results are proved about the way in which Boyland's forcing partial order organizes a set of braid types: those of periodic orbits of Smale's horseshoe map for which the associated train track is a star. This is a special case of a conjecture introduced in a previous paper, which claims that forcing organizes al…