arXiv subjects

Kentaro Hoshisashi

Publications and source records attributed to Kentaro Hoshisashi.

4 recordsLinked to original sources

arXiv2026

Fundamental Limits of Stability Inference in High-Dimensional Complex Systems

Many complex systems, including ecosystems, neural circuits, and financial markets, are inferred to operate close to a threshold of instability, at which a small perturbation can propagate across the entire system. This proximity is often interpreted as functionally advantageous, yet it poses a question common to all these fields: from a finite, noisy recording, how precisely can the distance of a system from that threshold be estimated? Using the multivariate Ornstein-Uhlenbeck process as the canonical linear model of relaxation near a stable fixed point, we show that the attainable precision is governed by three factors: an effective measurement budget, set by the number of samples relative to the system dimension and the sampling interval; the signal-to-noise ratio, given by the magnitude of deterministic interactions relative to stochastic forcing; and the distance to criticality, which simultaneously sets the system's correlation times and degrades both of the preceding factors. As the slowest dynamical mode softens near the threshold, the curvature of the log-likelihood flattens along the direction that determines stability, so that the relative uncertainty on the estimated distance diverges as that distance vanishes. Critically, temporal correlations near instability reduce the effective number of independent observations far below the nominal sample count, and inference breaks down when this effective count falls below the system dimension, even when the raw data volume appears sufficient. A direct consequence is the existence of an optimal sampling interval that diverges as the system approaches criticality, with practical implications for experimental design.

cond-mat.dis-nn↗

arXiv2026

Physics-Informed Neural Networks for Solving Derivative-Constrained PDEs

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as fundamental as the governing equations. In this paper, we present Derivative-Constrained PINNs (DC-PINNs), a general framework that treats constrained PDE solving as an optimisation guided by a minimum objective function criterion where the physics resides in the minimum principle. DC-PINNs embed general nonlinear constraints on states and derivatives, e.g., bounds, monotonicity, convexity, incompressibility, computed efficiently via automatic differentiation, and they employ self-adaptive loss balancing to tune the influence of each objective, reducing reliance on manual hyperparameters and problem-specific architectures. DC-PINNs consistently reduce constraint violations and improve physical fidelity versus baseline PINN variants, representative hard-constraint formulations on benchmarks, including heat diffusion with bounds, financial volatilities with arbitrage-free, and fluid flow with vortices shed. Explicitly encoding derivative constraints stabilises training and steers optimisation toward physically admissible minima even when the PDE residual alone is small, providing reliable solutions of constrained PDEs grounded in energy minimum principles.

cs.LG↗

arXiv2024

Whack-a-mole Online Learning: Physics-Informed Neural Network for Intraday Implied Volatility Surface

Calibrating the time-dependent Implied Volatility Surface (IVS) using sparse market data is an essential challenge in computational finance, particularly for real-time applications. This task requires not only fitting market data but also satisfying a specified partial differential equation (PDE) and no-arbitrage conditions modelled by differential inequalities. This paper proposes a novel Physics-Informed Neural Networks (PINNs) approach called Whack-a-mole Online Learning (WamOL) to address this multi-objective optimisation problem. WamOL integrates self-adaptive and auto-balancing processes for each loss term, efficiently reweighting objective functions to ensure smooth surface fitting while adhering to PDE and no-arbitrage constraints and updating for intraday predictions. In our experiments, WamOL demonstrates superior performance in calibrating intraday IVS from uneven and sparse market data, effectively capturing the dynamic evolution of option prices and associated risk profiles. This approach offers an efficient solution for intraday IVS calibration, extending PINNs applications and providing a method for real-time financial modelling.

q-fin.CP↗

arXiv2024

No-Arbitrage Deep Calibration for Volatility Smile and Skewness

Volatility smile and skewness are two key properties of option prices that are represented by the implied volatility (IV) surface. However, IV surface calibration through nonlinear interpolation is a complex problem due to several factors, including limited input data, low liquidity, and noise. Additionally, the calibrated surface must obey the fundamental financial principle of the absence of arbitrage, which can be modeled by various differential inequalities over the partial derivatives of the option price with respect to the expiration time and the strike price. To address these challenges, we have introduced a Derivative-Constrained Neural Network (DCNN), which is an enhancement of a multilayer perceptron (MLP) that incorporates derivatives in the objective function. DCNN allows us to generate a smooth surface and incorporate the no-arbitrage condition thanks to the derivative terms in the loss function. In numerical experiments, we train the model using prices generated with the SABR model to produce smile and skewness parameters. We carry out different settings to examine the stability of the calibrated model under different conditions. The results show that DCNNs improve the interpolation of the implied volatility surface with smile and skewness by integrating the computation of the derivatives, which are necessary and sufficient no-arbitrage conditions. The developed algorithm also offers practitioners an effective tool for understanding expected market dynamics and managing risk associated with volatility smile and skewness.

q-fin.CP↗