Universal probabilistic programming languages (PPLs) make it relatively easy to encode and automatically solve statistical inference problems. To solve inference problems, PPL implementations often apply Monte Carlo inference algorithms that rely on execution suspension. State-of-the-art solutions enable execution suspension either through (i) continuation-passing style (CPS) transformations or (ii) efficient, but comparatively complex, low-level solutions that are often not available in high-level languages. CPS transformations introduce overhead due to unnecessary closure allocations—a problem the PPL community has generally overlooked. To reduce overhead, we develop a new efficient selective CPS approach for PPLs. Specifically, we design a novel static suspension analysis technique that determines parts of programs that require suspension, given a particular inference algorithm. The analysis allows selectively CPS transforming the program only where necessary. We formally prove the correctness of the analysis and implement the analysis and transformation in the Miking CorePPL compiler. We evaluate the implementation for a large number of Monte Carlo inference algorithms on real-world models from phylogenetics, epidemiology, and topic modeling. The evaluation results demonstrate significant improvements across all models and inference algorithms.

Differential-Algebraic Equations (DAEs) are the foundation of high-level equation-based languages for modeling physical dynamical systems. Simulating models in such languages requires a transformation known as index reduction that involves differentiating individual equations before numerical integration. Commercial and open-source implementations typically perform index reduction by symbolic differentiation (SD) and produce a Jacobian callback function with forward-mode automatic differentiation (AD). The former results in efficient runtime code, and the latter is asymptotically efficient in both runtime and code size. However, AD introduces runtime overhead caused by a non-standard representation of real numbers, and SD is not always applicable in models with general recursion. This work proposes a new approach that uses partial evaluation of AD in the context of numerical DAE solving to combine the strengths of the two differentiation methods while mitigating their weaknesses. Moreover, our approach selectively specializes partial derivatives of the Jacobian by exploiting structural knowledge while respecting a user-defined bound on the code size. Our evaluation shows that the new method both enables expressive modeling from AD and retains the efficiency of SD for many practical applications.

Differential-algebraic equations, commonly used to model physical systems, are the basis for many equation-based object-oriented modeling languages. When systems described by such equations are influenced by unknown process disturbances, estimating unknown parameters from experimental data becomes difficult. This is because of problems with the existence of well-defined solutions and the computational tractability of estimators. In this paper, we propose a way to minimize a cost function-whose minimizer is a consistent estimator of the true parameters-using stochastic gradient descent. This approach scales significantly better with the number of unknown parameters than other currently available methods for the same type of problem. The performance of the method is demonstrated through a simulation study with three unknown parameters. The experiments show a significantly reduced variance of the estimator, compared to an output error method neglecting the influence of process disturbances, as well as an ability to reduce the estimation bias of parameters that the output error method particularly struggles with.

Differential-algebraic equations (DAEs) arise naturally as a result of equation-based object-oriented modeling. In many cases, these models contain unknown parameters that have to be estimated using experimental data. However, often the system is subject to unknown disturbances which, if not taken into account in the estimation, can severely affect the model's accuracy. For non-linear state-space models, particle filter methods have been developed to tackle this issue. Unfortunately, applying such methods to non-linear DAEs requires a transformation into a state-space form, which is particularly difficult to obtain for models with process disturbances. In this paper, we propose a simulation-based prediction error method that can be used for non-linear DAEs where disturbances are modeled as continuous-time stochastic processes. To the authors' best knowledge, there are no general methods successfully dealing with parameter estimation for this type of model. One of the challenges in particle filtering  methods are random variations in the minimized cost function due to the nature of the algorithm. In our approach, a similar phenomenon occurs and we explicitly consider how to sample the underlying continuous process to mitigate this problem. The method is illustrated numerically on a pendulum example. The results suggest that the method is able to deliver consistent estimates.

Recent years are characterized by a growing digitalization of production environment and other areas of human's life. Complex cyber-physical systems play a very important role within this development. Hence, integrated model-based design of such systems has gained significant attention. Quite naturally, this leads to the necessity of modeling hybrid system - systems containing both continuous-time and event-based phenomena. Hybrid modeling languages based on equations, supporting both continuous-time and eventbased aspects (e.g. Modelica, SysML, VHDL-AMS, and Simulink/Simscape) enable high-level reuse and integrated modeling capabilities of both the physically surrounding system and software for embedded systems. Using such equation-based object-oriented (EOO) modeling languages, it has become feasible to model complex systems covering multiple application domains at a high level of abstraction through reusable model components. They thus offer considerable advantages for many application areas. EOOLT is a forum for researchers with interests in all aspects of equation-based modeling languages and their supporting tools, including design, implementation, open issues limiting their expressiveness or usefulness, as well as novel applications.

Probabilistic programming languages (PPLs) make encoding and automatically solving statistical inference problems relatively easy by separating models from the inference algorithm. A popular choice for solving inference problems is to use Monte Carlo inference algorithms. For higher-order functional PPLs, these inference algorithms rely on execution suspension to perform inference, most often enabled through a full continuation-passing style (CPS) transformation. However, standard CPS transformations for PPL compilers introduce significant overhead, a problem the community has generally overlooked. State-of-the-art solutions either perform complete CPS transformations with performance penalties due to unnecessary closure allocations or use efficient, but complex, low-level solutions that are often not available in high-level languages. In contrast to prior work, we develop a new approach that is both efficient and easy to implement using higher-order languages. Specifically, we design a novel static suspension analysis technique that determines the parts of a program that require suspension, given a particular inference algorithm. The analysis result allows selectively CPS transforming the program only where necessary. We formally prove the correctness of the suspension analysis and implement both the suspension analysis and selective CPS transformation in the Miking CorePPL compiler. We evaluate the implementation for a large number of Monte Carlo inference algorithms on real-world models from phylogenetics, epidemiology, and topic modeling. The evaluation results demonstrate significant improvements across all models and inference algorithms.