#01Oct 30, 2026
physics.flu-dyn
Hard Constraint Projection in a Physics Informed Neural Network (Burgers)
Miranda J S Horne, Peter K Jimack, Amirul Khan and 1 more
Physics informed machine learning provides a framework to study and simulate fluid dynamics, potentially at a fraction of the computational cost of traditional numerical methods, with the goal of improving the explainability, accuracy and robustness of purely data driven machine learning methods. In this work, we extend the hard constraint projection (HCP) method developed by Chen et al. [Journal of Computational Physics, 445, 110624, 2021] from a linear partial differential equation (PDE) to a nonlinear PDE: the 1D Burgers' equation. To strictly impose a discrete approximation of the governing equation, the Burgers' equation is first locally discretised (using a finite difference stencil) then decomposed into a constraint matrix and a prediction matrix. Using tools from linear algebra, the constraint matrix is used to construct a projection matrix. A physics informed neural network (PINN) [Raissi et al. Journal of Computational Physics, 378, 686, 2019] is used to predict the velocity, and a final unlearnable layer projects the velocity prediction to the hyperplane of exact solutions to a discretised form of the Burgers' equation. Our initial results indicate that the HCP-PINN initially trains similarly to an equivalent PINN, and as the PINN loss plateaus, the HCP-PINN loss continues to decline. When tested on a previously unseen uniform grid of points covering the domain, the HCP-PINN exhibits higher accuracy, converging to a data error approximately an order of magnitude lower than the comparable PINN. We also observe that the inclusion of the HCP layer results in better observance of the governing PDE. Our findings suggest that the HCP-PINN can be more robust to the selection of physics collocation points, and less dependent on collocation point quantity.
#02Oct 30, 2026
cs.LG
Fast Privacy Loss Accounting for Random Allocation via Multiscale FFT
Vitaly Feldman, Moshe Shenfeld
In the random allocation sampling scheme each user's data is used in $k$ steps chosen randomly and uniformly from a sequence of $t$ steps. This scheme is known to improve on Poisson sampling in private optimization and in communication-efficient aggregation. The existing privacy loss distribution (PLD) accountant for this scheme runs in time quadratic in the inverse of the accuracy parameter $α$ (Feldman and Shenfeld, 2026). We give an algorithm, \emph{multiscale FFT}, that represents likelihood ratios on a grid that is uniform within each dyadic interval and computes the exact rounding of every pairwise sum using FFTs within each interval. It keeps the guarantees of the accountant and improves the dependence of its running time on $α$ from $O(α^{-2})$ to $O(α^{-1}\log(1/α))$. In addition, we demonstrate that rounding can be performed via the mean-preserving connect-the-dots projection of (Doroshenko et al., 2026). This reduces the errors that rounding introduces in the mean of the privacy loss and in the $χ^2$ divergence of the computed pair from the order of $α$ to $O(α^2/\log(t))$. In our experiments, our algorithm achieves speedups of several orders of magnitude at high accuracy and gives improved privacy bounds for DP-SGD with PREAMBLE.
#03Oct 30, 2026
cs.AI
Same Question, Different Answers: Auditing Persona-Dependent Variation in Six LLMs on Smoking-Cessation Advice
Artin Yousefi, Aizierjiang Aiersilan, Lorien C Abroms and 1 more
Hundreds of millions of people now ask large language model (LLM) chatbots for health advice, which raises a question that is simple to pose and hard to answer: does everyone get the same advice? We audit six widely deployed LLMs from four providers on smoking cessation, a domain with codified clini- cal guidance and substantial public-health stakes, by putting the same four cessation questions to twelve user personas that differ in life stage, self-described expertise, and smoking history, for a total of 2,880 responses. What the models say depends on who appears to be asking. Every model named FDA-approved prescription cessation medications less often to teen personas than to adult personas, by 32 to 67 percentage points, and in five of six models a persona presenting health- care expertise received fewer facts than a persona presenting none. We then evaluate one deployable intervention: a short system prompt specifying a factual floor, the set of core med- ical facts every user should receive when they are relevant, while leaving tone, vocabulary, and framing free to adapt. The prompt narrows persona differences in every model, but its effect on overall fact coverage varies in both magnitude and direction across models, so a prompt validated on one system cannot be assumed to transfer to another. Two cautions frame these results. Equal mention rates are not always the correct clinical target, because prescription cessation pharmacother- apy is not recommended for minors, so a defensible factual floor must be age-aware rather than uniform. And because our personas vary on several attributes at once, we report scenario- level differences rather than isolated effects of age or expertise. We release all 2,880 responses and the analysis code.
#04Oct 30, 2026
cs.LG
Instance-dependent sequential limits as an exact information ledger
Akshay Balsubramani
Instance-dependent limits for bandit regret, sequential tests, best-arm identification and Markov decision processes are proved by one chain. It runs from a divergence decomposition through data processing to a statistic, a testing step that turns a class guarantee into a requirement on the history, and optimization over alternatives and allocations. Only the first step is an identity. This work writes the chain as an exact ledger. By the chain rule, data processing loses exactly a conditional divergence, which vanishes for arms in natural exponential families at the per-arm counts and reward sums. A one-parameter family of martingale identities extends the decomposition to every tilt between two instances. The classical limits follow by relaxations with named defects. All defects but the asymptotic step's can be computed from an algorithm's own runs, the uniform quantification's only when the class guarantee is a number. On seven published sources, from movie ratings to engine replacement, the ledger locates the difference between standard algorithms and the classical limits. For identification among trained models and for Wald's test the largest term is usually the uniform quantification's.
#05Oct 30, 2026
cs.LG
Physiological Trajectories and Observation Patterns in ICU Mortality Prediction: Transportability Under Changing Measurement Conditions
Benjamin T. Pike
Objective: To distinguish the transferable predictive value of physiological trajectories from that of observation patterns in ICU mortality prediction, and to assess whether measurement timing affects performance independently of observation quantity. Materials and Methods: In-hospital mortality was predicted at 48 hours using MIMIC-III, MIMIC-IV, and eICU. Nested representations progressively integrated latest-value snapshots (R1), longitudinal physiological summaries (R2), and measurement frequency and timing features (R3). Models fitted on 7,762 MetaVision patients were evaluated on 21,682 MIMIC-IV patients and 43,878 eICU patients across 204 hospitals. The effect of measurement timing was assessed while holding the number of retained observations constant. Results: Physiological trajectories improved external prediction in eICU (R2-R1 log-loss difference -0.00922, 95% CI -0.01148 to -0.00704). Observation-pattern features improved locally developed eICU models (R3-R2 -0.00257, 95% CI -0.00370 to -0.00146), but not clearly after transfer from MetaVision (-0.00012, 95% CI -0.00206 to +0.00208). R3 was favoured in 10 of 30 source bootstrap refits. At matched observation counts, retaining measurements spread throughout the window reduced log loss relative to random retention by 0.03280 for R3 versus 0.00703 for R2. Removing the final 12 hours increased log loss relative to count-matched random removal by 0.01947 for R3 versus 0.00822 for R2. Under reduced availability, the local R3 increment changed from beneficial to harmful. Discussion: Physiological trajectories transferred more consistently, while observation-pattern features were particularly sensitive to the timing and availability of measurements. Conclusion: Clinical prediction models should be evaluated not only in new patient populations but also under the measurement conditions that supply their inputs.