Adjoint SA speeds up bioprocess parameter learning.
problem Challenges in digital twin development for biomanufacturing.
method Adjoint sensitivity analysis on multi-scale enzymatic reaction networks.
result Resilient sensitivities reveal bioprocess regulatory mechanisms.
This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This is due to the mixed Lagrangian-Eulerian formulation of large-displacement FSI in…
SNAPO optimizes policies for complex sequential decisions using differentiable simulation.
problem Optimizing policies for high-dimensional, sequential decisions under uncertainty.
method Embeds neural policy in a differentiable simulator, computes gradients efficiently.
result Produces sensitivities at a cost proportional to one reverse pass, regardless of sensitivity count.
Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic differentiation, techniques to calcul…
Framework calculates positional influence in causal residual Transformers.
problem Understanding positional influence in causal residual Transformers.
method Adjoint-sensitivity framework for positional influence in causal residual Transformers.
result Exact evolution of adjoint-energy influence density and decomposition into residual transmission, nonlocal Volterra, and local channels.
New method reduces errors in pricing and sensitivities for discontinuous payoffs.
problem Errors in pricing and sensitivities for discontinuous payoffs in digital and barrier options.
method Alternative methods for estimating sensitivities, including likelihood ratio and hybrid methods.
result New methods substantially reduce test errors in prices and sensitivities.
NDDV estimates data point value from a single stochastic trajectory.
problem Estimating marginal contributions of data points over stochastic training paths.
method Introduces Neural Dynamic Data Valuation (NDDV) using stochastic state and adjoint equations.
result NDDV provides a one-run, trajectory-conditioned estimator of data point value.
Using Roelcke formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface X and compute the S-matrix of X at the zero value of the spectral parameter. We apply these results to study various self-adjoint extensions of a symmetric Laplacian…
Framework for pricing waterfall structures using simulation and uncertainty modeling.
problem Pricing complex structured finance instruments under uncertainty.
method Simulation-based uncertainty modeling, calibrated probability distributions, PyTorch implementation, Adjoint Algorithmic Differentiation (AAD).
result Efficient gradient computation for risk sensitivity analysis and optimization.
SDE Matching eliminates simulation for training Latent SDEs, achieving similar performance.
problem Training Latent SDEs with adjoint sensitivity methods is computationally expensive and limited.
method SDE Matching, inspired by Score- and Flow Matching, eliminates simulation for training Latent SDEs.
result SDE Matching achieves performance comparable to adjoint sensitivity methods while reducing computational complexity.
Stable neural flows ensure robustness and efficiency in deep learning.
problem Ensuring robustness and stability in deep learning models.
method Introducing a stable variant of neural ODEs with a neural network parametrizing an energy functional, solving as an optimal control problem with adjoint sensitivity analysis.
result The proposed model provides robustness against input perturbations and low computational burden.
We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to simultaneously achieve computational efficiency and accurate confidence intervals. We illus…
New framework for higher-order singular-value derivatives of rectangular matrices.
problem Challenging to derive higher-order Fréchet derivatives of singular values in real rectangular matrices.
method Using Kato's analytic perturbation theory for self-adjoint operators and embedding rectangular matrices into block self-adjoint operators.
result Closed-form expressions for the n-th order spectral variations of singular values. Study cash-flow forecasting for derivatives, aligning with replication strategy and addressing timing frictions.
problem Inconsistencies in cash-flow forecasting under different measures and stochastic payment times.
method Use discounting sensitivities (funding-curve hedge ratios) for replication and propose a liquidity valuation adjustment.
result Aligns forecasting with replication strategy and avoids measure-mixing issues.
SONODEs and ANODEs improve learning of second order dynamics.
problem Learning dynamics governed by second order laws.
method Extended adjoint sensitivity method and theoretical analysis of ANODEs.
result SONODEs and ANODEs can learn higher order dynamics efficiently.
New method optimizes fairness in predictive models for continuous sensitive attributes.
problem Enforcing full statistical independence on continuous sensitive attributes is too restrictive.
method Functional bilevel optimization (FBO) and ITD algorithms.
result Achieves lowest or near-lowest fairness-accuracy regret on synthetic and real datasets.
Neural DEs improve single image super-resolution.
problem Challenging tasks in image super-resolution.
method Applied Neural Differential Equations to image super-resolution, using variational methods and backpropagation.
result Differential models match state-of-the-art performance.
Optimizes portfolios using neural network approximations of asset sensitivities to common drivers.
problem Optimizing portfolios with complex asset dynamics and common drivers.
method Model asset dynamics with PDEs, approximate sensitivities with neural networks, and use hierarchical clustering on sensitivity matrix for optimization.
result Achieves over-performance in portfolio optimization across various markets and datasets.
Proposes a method to improve surrogate models by incorporating sensitivity information.
problem Pruned neural networks often fail to capture sensitivities and uncertainties of original models.
method Combines Interval Adjoint Significance Analysis and Sobolev Training to accurately model sensitivities.
result Pruned models based on the proposed method better match original sensitivities.
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differen…
Derives adjoint polynomials of torus knots in explicit form.
problem Understanding adjoint invariants of torus knots.
method Closed-form double sum expression derivation.
result Explicit double sum form of adjoint polynomials.
We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.
Proves formal self-adjointness of certain differential operators.
problem Verifying conjectures about differential operators.
method Proving formal self-adjointness through mathematical proof.
result Proves two conjectures about differential operators.
Gradient flow autoencoder improves data efficiency over traditional autoencoders.
problem Sub-optimal latent space representations in autoencoders.
method Gradient flow through ODE with adaptive step size for optimization.
result Gradient flow autoencoder achieves higher data efficiency.
Study of adjoint orbits in simplest non-trivial Lie algebra case.
problem Geometric properties of adjoint orbits in sl(2,R). method Analysis of adjoint orbits, showing three possibilities: hyperboloids or cones.
result Just three possibilities for adjoint orbits: hyperboloids or cones.
Abstracts a construction of boundary triplets for self-adjoint elliptic problems.
problem Computing the index of families of self-adjoint elliptic boundary problems.
method Abstract axiomatic version of boundary triplets and their applications.
result Analytic proof of index theorem and computation of index differences.
Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians.
problem Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians. method Consider the sum of the adjoint Reidemeister torsions and prove integrality for twist knots and meridians.
result Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians. Quantizes Stäckel integrable systems into self-adjoint operators.
problem Quantizing Stäckel integrable systems into self-adjoint operators.
method Constructs commutative self-adjoint operators from quadratic Hamiltonians in involution.
result Proves multiplicative separation of variables for Stäckel integrable systems.
We give explicit descriptions of the adjoint group of the Coxeter quandle QW associated with an arbitrary Coxeter group W. The adjoint group of QW turns out to be an intermediate group between W and the corresponding Artin group AW, and fits into a central extension of W by a finitely generated free abel…
Paper analyzes double twist knots using adjoint hyperbolic torsion polynomial.
problem Determining the genus and fibering of double twist knots.
method Uses adjoint hyperbolic torsion polynomial to analyze double twist knots.
result The adjoint hyperbolic torsion polynomial determines the genus and fibering of double twist knots.
Derives adjoint formulas for matrix operations and applies them to specific cases.
problem Computing adjoints for matrix operations and specific matrix types.
method Derives adjoint formulas for matrix operations and applies them to specific cases.
result Closed-form expressions for adjoints in specific matrix types.
Explicit formula for Reidemeister torsion of two-bridge knots.
problem Calculating Reidemeister torsion for two-bridge knots.
method Provided an explicit formula and proved vanishing identities.
result Adjoint Reidemeister torsion satisfies vanishing identities.
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in p…
The paper explores self-adjointness of Laplace-Beltrami operator on special geometric manifolds.
problem Characterizing self-adjoint extensions of the Laplace-Beltrami operator on α-Grushin manifolds. method Introducing an exotic calculus of pseudodifferential operators adapted to the geometry of the singularity.
result Criterion for essential self-adjointness and determination of several self-adjoint extensions.
Study extends Vogel's universality to torus knots in adjoint representation.
problem Applying Vogel's universality to knot invariants in adjoint representation theory.
method Extending Vogel's parameters to include torus knots T[m,n] and focusing on T[4,n] with odd n. result Unified description of adjoint invariants for torus knots T[4,n] with odd n. QMC and GSA improve option pricing and risk measures efficiency.
problem Efficiently pricing and hedging complex financial instruments.
method Application of QMC and GSA techniques for financial instrument pricing and hedging, comparing MC vs QMC and analyzing greeks computation.
result QMC outperforms MC in most cases, especially in high-dimensional simulations, leading to faster and more stable convergence.
Extends adjoint representation concept to higher Lie groupoids.
problem Defining adjoint representation for higher Lie groupoids.
method Generalizes standard construction to higher Lie groupoids using simplicial vector bundles.
result Adjoint representation up to homotopy is well-defined and unique.
New knot theory module shows torsion-ness in number theory.
problem Torsion-ness of Selmer modules in Galois representations.
method Introducing adjoint homological Selmer module for SL2-representations of knot groups. result Finitely generated torsion-ness of the new Selmer module.
We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of ana…
The study confirms essential self-adjointness for certain differential operators on manifolds.
problem Essential self-adjointness of differential operators on closed manifolds.
method Analyzing the Hamiltonian flow of the symbol of differential operators.
result The conjecture that certain differential operators are essentially self-adjoint if their Hamiltonian flow is complete.
Paper proves index theorem for self-adjoint elliptic boundary problems.
problem Proving index theorem for self-adjoint elliptic boundary problems.
method Topological and pseudo-differential methods, generalized Atiyah-Singer approach.
result Removed technical assumption to prove index theorem.
Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.
problem Limited theory and algorithms for sampling infinite-dimensional function spaces.
method Adjoint Sampler for infinite-dimensional function spaces based on stochastic maximum principle.
result FAS achieves superior performance in synthetic and real systems.
Let Δ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold M. One can consider a pencil of operators $\hPi(Δ)=\{Δ_ł\}$ passing through the operator Δ such that any Δł is a linear differential operator acting on densities of weight ł. This pencil can be iden…
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boun…
I show that the adjoint variety of the complex special linear group is rigid to order three.
We give explicit formulas for the adjoint twisted Alexander polynomial and the nonabelian Reidemeister torsion of genus one two-bridge knots.
The study finds Lagrangian submanifolds in adjoint semisimple orbits for real forms.
problem Characterizing Lagrangian submanifolds in adjoint semisimple orbits.
method Analyzing real flags and orbits of real forms with respect to symplectic forms.
result Classification of infinitesimally tight Lagrangian submanifolds in the compact case and Lagrangian submanifolds in the complex case.
Unified framework extends adjoint Schrödinger bridge sampler to discrete spaces.
problem Challenges in learning discrete neural samplers due to gradients and combinatorial complexity.
method Introduces discrete ASBS, a unified framework that extends adjoint Schrödinger bridge sampler to discrete spaces.
result Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.