| 1. |
- Murray, Lawrence, et al.
(författare)
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Delayed sampling and automatic Rao-Blackwellization of probabilistic programs
- 2018
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Ingår i: Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS), Lanzarote, Spain, April, 2018. - : PMLR.
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Konferensbidrag (refereegranskat)abstract
- We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with Sequential Monte Carlo, this automatically yields improvements such as locallyoptimal proposals and Rao–Blackwellization. The mechanism maintains a directed graph alongside the running program that evolves dynamically as operations are triggered upon it. Nodes of the graph represent random variables, edges the analytically-tractable relationships between them. Random variables remain in the graph for as long as possible, to be sampled only when they are used by the program in a way that cannot be resolved analytically. In the meantime, they are conditioned on as many observations as possible. We demonstrate the mechanism with a few pedagogical examples, as well as a linearnonlinear state-space model with simulated data, and an epidemiological model with real data of a dengue outbreak in Micronesia. In all cases one or more variables are automatically marginalized out to significantly reduce variance in estimates of the marginal likelihood, in the final case facilitating a randomweight or pseudo-marginal-type importance sampler for parameter estimation. We have implemented the approach in Anglican and a new probabilistic programming language called Birch.
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| 2. |
- Abdalmoaty, Mohamed R. H., 1986-, et al.
(författare)
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Identification of Non-Linear Differential-Algebraic Equation Models with Process Disturbances
- 2021
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Ingår i: 2021 60th IEEE Conference on Decision and Control (CDC). - : IEEE. - 9781665436595 - 9781665436588 - 9781665436601 ; , s. 2300-2305
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 3. |
- Aronsson, Peter, et al.
(författare)
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Extendable Physical Unit Checking with Understandable Error Reporting
- 2009
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Ingår i: Proceedings of the 7th International Modelica Conference. - Linköping : Linköping University Electronic Press, Linköpings universitet. - 9789173935135 ; , s. 890-897
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Konferensbidrag (refereegranskat)abstract
- Dimensional analysis and physical unit checking are important tools for helping users to detect and correct mistakes in dynamic mathematical models. To make tools useful in a broad range of domains, it is important to also support other units than the SI standard. For instance, such units are common in biochemical or financial modeling. Furthermore, if two or more units turn out be in conflict after checking, it is vital that the reported unit information is given in an understandable format for the user, e.g., “N.m” should preferably be shown instead of “m2.kg.s-2”, even if they represent the same unit. Presently, there is no standardized solution to handle these problems for Modelica models. The contribution presented in this paper is twofold. Firstly, we propose an extension to the Modelica language that makes it possible for a library designer to define both new base units and derived units within Modelica models and packets. Today this information is implicitly defined in the specification. Secondly, we describe and analyze a solution to the problem of presenting units to users in a more convenient way, based on an algorithm using Mixed Integer Programming (MIP). Both solutions are implemented, tested, and illustrated with several examples.
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| 4. |
- Bereza-Jarocinski, Robert, et al.
(författare)
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Stochastic Approximation for Identification of Non-Linear Differential-Algebraic Equations with Process Disturbances
- 2022
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Ingår i: 2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781665467612 - 9781665467605 - 9781665467629 ; , s. 6712-6717
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 5. |
- Broman, David, 1977-, et al.
(författare)
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A comparison of two metacompilation approaches to implementing a complex domaispecific language
- 2012
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Ingår i: Proceedings of the 27th Annual ACM Symposium on Applied Computing (SAC). - New York, NY, USA : ACM. - 9781450308571 ; , s. 1919-1921
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Konferensbidrag (refereegranskat)abstract
- Operational semantics and attribute grammars are examples of formalisms that can be used for generating compilers. We are interested in finding similarities and differences in how these approaches are applied to complex languages, and for generating compilers of such maturity that they have users in industry.As a specific case, we present a comparative analysis of two compilers for Modelica, a language for physical modeling, and which contains numerous compilation challenges. The two compilers are OpenModelica, which is based on big-step operational semantics, and JModelica.org, which is based on reference attribute grammars.
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| 6. |
- Broman, David, 1977-
(författare)
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A vision of miking : Interactive programmatic modeling, sound language composition, and self-learning compilation
- 2019
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Ingår i: SLE 2019 - Proceedings of the 12th ACM SIGPLAN International Conference on Software Language Engineering, co-located with SPLASH 2019. - New York, NY, USA : Association for Computing Machinery, Inc. - 9781450369817 ; , s. 55-60
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Konferensbidrag (refereegranskat)abstract
- This paper introduces a vision of Miking, a language framework for constructing efficient and sound language environments and compilers for domain-specific modeling languages. In particular, this language framework has three key objectives: (i) to automatically generate interactive programmatic modeling environments, (ii) to guarantee sound compositions of language fragments that enable both rapid and safe domain-specific language development, (iii) to include first-class support for self-learning compilation, targeting heterogeneous execution platforms. The initiative is motivated in the domain of mathematical modeling languages. Specifically, two different example domains are discussed: (i) modeling, simulation, and verification of cyber-physical systems, and (ii) domain-specific differentiable probabilistic programming. The paper describes the main objectives of the vision, as well as concrete research challenges and research directions.
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| 7. |
- Broman, David, 1977-, et al.
(författare)
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Abstract Syntax Can Make the Definition of Modelica Less Abstract
- 2007
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Ingår i: Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools, Berlin, Germany. - 9789175198224 ; , s. 111-126
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Konferensbidrag (refereegranskat)abstract
- Modelica is an open standardized language used for modeling and simulation of complex physical systems. The language specification defines a formal concrete syntax, but the semantics is informally described using natural language. The latter makes the language hard to interpret, maintain and reason about, which affect both tool development and language evolution. Even if a completely formal semantics of the Modelica language can be seen as a natural goal, it is a well-known fact that defining understandable and concise formal semantics specifications for large and complex languages is a very hard problem. In this paper, we will discuss different aspects of formulating a Modelica specification; both in terms of what should be specified and how it can be done. Moreover, we will further argue that a “middle-way” strategy can make the specification both clearer and easier to reason about. A proposal is outlined, where the current informally specified semantics is complemented with several grammars, specifying intermediate representations of abstract syntax. We believe that this kind of evolutionary strategy is easier to gain acceptance for, and is more realistic in the short-term, than a revolutionary approach of using a fully formal semantics definition of the language.
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| 8. |
- Broman, David, 1977-, et al.
(författare)
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Design Considerations for Dimensional Inference and Unit Consistency Checking in Modelica
- 2008
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Ingår i: Proceedings of the 6th International Modelica Conference. - Bielefeld, Germany : Modelica Association. ; , s. 3-12
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Konferensbidrag (refereegranskat)abstract
- The Modelica language supports syntax for declaring physical units of variables, but it does not yet exist any defined semantics for how dimensional and unit consistency checking should be carried out. In this paper we explore different approaches and new constructs for improved dimensional inference and unit consistency checking in Modelica; both from an end-user, library, and tool perspective. A proposal for how dimensional inference and unit checking can be carried out is outlined and a prototype implementation is developed and verified using several examples from the Modelica standard library.
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| 9. |
- Broman, David, 1977-, et al.
(författare)
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Determining Over- and Under-Constrained Systems of Equations using Structural Constraint Delta
- 2006
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Ingår i: Proceedings of the 5th International Conference on Generative Programming and Component Engineering. - New York, NY, USA : ACM. ; , s. 151-160
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Konferensbidrag (refereegranskat)abstract
- Computer aided modeling and simulation of complex physical systems, using components from multiple application domains, such as electrical, mechanical, and hydraulic, have in recent years witnessed a significant growth of interest. In the last decade, equation-based object-oriented (EOO) modeling languages, (e.g. Modelica, gPROMS, and VHDL-AMS) based on acausal modeling using Differential Algebraic Equations (DAEs), have appeared. With such languages, it is possible to model physical systems at a high level of abstraction by using reusable components.A model in an EOO language needs to have the same number of equations as unknowns. A previously unsolved problem concerning this property is the efficient detection of over- or under-constrained models in the case of separately compiled models.This paper describes a novel technique to determine over- and under-constrained systems of equations in models, based on a concept called structural constraint delta. In many cases it is also possible to locate the source of the constraint-problem. Our approach makes use of static type checking and consists of a type inference algorithm. We have implemented it for a subset of the Modelica language, and successfully validated it on several examples.
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| 10. |
- Broman, David, 1977-, et al.
(författare)
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Functional programmatic modeling in modelyze
- 2019
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Ingår i: ACM International Conference Proceeding Series. - New York, NY, USA : Association for Computing Machinery. - 9781450377133
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Konferensbidrag (refereegranskat)abstract
- 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.
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